Jojo_Fr wanted me to write this thread which make a comparison between upgrade and buyout cost as there may be some interesting issues when you compare those. To read how buyout cost works, read this.

Upgrade cost work in a much simpler way, upgrade cost is equal to the industry cost of the unit you upgrade to, it don't matter what the unit you upgrade is for something, like upgrading a scout or horsemen to knight cost the same 800 money (knight cost 800 industry). This make it obvious to spam old cheap obsolete units such as scouts and maintain a tech path that allow you to build them for a long time, such as not researching mounted warfare as that replace your ability to build scouts with horsemen. Anyway how cheap is upgrade cost compared to buyout cost, lets look at some graphs, to make it simple I removed the buyout inflation, so this is the best case for buyout:

 The graph show the total money cost (horizontal axis) to buy or upgrade to an unit with the industry cost (vertical axis). The blue line is the buyout cost and the red line is the upgrade cost, as can be seen the buyout cost is far higher than the upgrade cost and the yellow line which I took buyout cost minus upgrade cost is not that much lower than the buyout cost. Buying an unit that cost 5000 industry is about twice as expensive compared to upgrading to an 15000 industry unit.

So now we may ask, since upgrade replace one unit with another, maybe buyout is not as bad, like if I have a scout and upgrade to a knight, I now have a knight but no scout. If I buy a knight I keep my scout, lets look at the diagram in which I specifically check the scout line and compare the cost of buying a new unit vs buying older units and upgrade it to the new unit, in both cases we have ended up with one unit, but what is cheaper. Inflation can be ignored in this case as we pay it once in all 3 cases in the diagram:

The blue column show how much it cost to buy the unit directly. The red column show how much it cost to buy a scout and upgrade it to the unit. The yellow column show how much it cost to purchase the previous unit such as a horsemen and upgrade it to a knights. As can be seen buying scouts and upgrade them is very cheap, far cheaper than purchasing the unit directly. It is also cheaper in all cases to buy the older unit and upgrade it, only helicopter gunship is close. 

We can reduce unit industry cost with things such as legacy traits and infrastructure and the next diagram show how the cost would be with all unit cost reducing infrastructure built:

While buyout cost look better, it is still the most expensive, except in the helicopter gunship case in which it perform just slightly better than buying a dragoons and upgrade it to a helicopter gunship.

This don't even take in account that upgrade have some other advantages such as if the unit you upgrade to cost more pops, those pops are gained for free, you can move the obsolete units in position and upgrade them instantly to make for fast wars and upgrade heals damaged units to full hitpoints.

Now this graph which show how much money you spend on each industry you buyout. It give an idea why buyout is so expensive compared to upgrade cost:

You can see that buyout will pretty much always cost atleast twice as much money as the industry cost and for more expensive units this can reach above a 5 money per industry ratio. Upgrade cost is always equal to the base industry cost of unit, thus a one to one ratio of industry to money, except you lose the old unit, but also gain population in certain cases.

We also should not forget that buyout have inflation based on which turn the game is at, upgrade do not have any inflation and the inflation cost look like this:

The inflation can increase the buyout cost, especially for low industry items by alot overtime, thus you would likely produce and upgrade rather than buyout and upgrade to maximize the value of your money and industry. Building scouts and upgrade them to knights would be a low cost in both industry and money and also make a one pop cost unit into a two pop cost unit, thus creating population for you.

Anyway I think we can be quite safe to say that upgrading is a better use than buying units directly, producing long since obsolete units that are cheap and upgrade them seems to be an very effective way to spend your money and industry on and may give the players who take advantage of this a huge advantage of those that don't.

Now is this a good thing, that upgrade cost is so much cheaper than buyout cost, that I guess you can tell me.

IMHO the issue here mostly lies in the scaling inflation of the Buyout Cost. Upgrade Cost is still relatively expensive (using a 1:1 ratio for Money:Industry) in the early game, but in comparison with the massive Buyout inflation (the ratio can be up to at least 6:1) in the late game, the Upgrade Cost becomes seemingly much cheaper.

Goodluck why are you comparing buyout cost to upgrading, instead of usefullness of producing unit vs upgrading it? and how feasible it is to have enough money to upgrade later game units?

I would personally prefer if upgrading of units had to take place in cities (or maybe admin centers), cost 100% movement and would subtract population from the city if the new unit had a higher pop cost. This would solve most of the potentially abusive mechanics of upgrading in its current form.

As for upgrading costs being more monetarily efficient than rushing production of a unit for cash
VS
Upgrading costs being too expensive in later eras. I feel that the cost could probably be safely reduced if the changes i mentioned above were made. Additionally the cost could be the sum-total of upgrade costs for all intermediary units. So it would essentially be upgrading scout > horse > knight > dragoon > helicopter all combined, but with only 1 button click. This would make it no longer beneficial to sit on ancient obsolete units until it came time to upgrade in one fell swoop. This removes the effective monetary penalty for keeping your army up to date. With this there would be no reason NOT to upgrade a unit as soon as an upgrade came available, rather than waiting for an even more advanced tier to unlock.

Another possible idea would be to add a penalty cost for upgrading more than one tier at at time.

So, if you upgrade from scout > horse = cheap

But if you upgrade from scout > knight it would cost significantly more than the sum of scout > horse & horse > knight

So you could make it so that scout > helicopter scales so high that.... well, you could never afford it.

If you think about it, this sorta makes sense. It would be easier to retrain an axeman to use a sword, than to train an axeman to use a machine gun.

If these changes were made, yes, technically the monetary cost to buy out an old unit and then upgrade to a modern one would still be cheaper, but since it could only be done once per game (since you cannot un-learn a tech once attained), it might feel less weird.

The game requires you to find "broken" mechanics and exploit them. It's a lot like Slay the Spire in that respect. A straightforward linear improvement to your civ (or deck) will simply lose in the end to the viciously unfair contemporary era (massive improbable heart).

That's why upgrading in the late game can feel expensive, even if we have a graph showing it's the most efficient use of money.

That's also why so many games end when the player realizes that they should just concede because they didn't get a scaling engine going. The simplest scaling engine is industry, so then some of them come back to complain that industry is completely broken. It's a bit broken, but it's kinda intentional -- the key is to make sure there are scaling engines for money, science, influence and population (single-city pop doesn't scale, intentionally, but you can get a nice big population via expansion).

Buyouts are insanely expensive in the late game because the devs didn't want money-scaling civs to just buy an entire giant army in one turn. And you can easily have 100K money in the bank if that was your intent. 

Upgrade cost is alright, buyout is completely bonkers. They nerved it into oblivion after it had been OP in the opendev. Kinda makes me think the devs don't know what they're doing, unfortunately.