Looking through the Technologies required for nuclear weapons and nuclear fusion is concerning because they are completely isolated from the rest of the tech tree.

Research institute has no prerequisite technologies needed to research it, so it can be researched as soon as the player enters the contemporary era, which is a big problem because it can be accessed far sooner than it likely should be through players or AI ascending through eras quickly.
For example, you could still only have medieval or early modern era technologies but still be able to have access to research institute.
With no other tech requirements for nuclear weapons, players and AIs can get access to nukes very quickly, much faster than likely intended if they have this strategy in mind combined with prioritizing science and industry
A second massive design issue that is compounded by this is the ease of access to nuclear fusion
The entire contemporary era tech tree can be skipped outside of the three nuclear technologies to acquire its extremely powerful +50% industry bonus extremely quickly, easily allowing the player to snowball their FIMSI output and produce nuclear weapons at a much faster pace than what is intended.
The lack of tech requirements for these game changing techs creates a strategy so lucrative it could easily become too meta compared to everything else and hamper variety in gameplay.
However, I think the solution to this gargantuan issue is very simple
All that would be required is introducing two technology prerequisites.
First, adding a requirement of wireless telegraphy to work on research institute to ensure a players science is up to speed to grab it.
And second, adding either renewable energy or world wide web as a requirement for Fusion reactor. This would ensure the player actually has to substantially work through the contemporary era tech tree in order to access the very lucrative bonuses this technology provides.
On a second note, the final 5 futuristic technologies seem to have a very low technology cost compared to their uniqueness and power.
Pretty much any culture with a modest science output can gain access to them if they so choose.
They do not feel like a substantial step up from the rest of the tech tree with only a minor increase in cost.
Massively increasing the costs for Exosuit, Space Orbital, Military Laser, Neural Implant, and Fusion Reactor would create more of an incentive to pick scientist cultures, by effectively making them the only ones able to create a science output great enough to obtain these powerful techs.
Another possible solution is to lock the 5 techs into an entirely separate "era" and having only the science cultures with their foresight affinity bonus able to research them.
Overall, I think the solution to the central issue is very simple and wouldn't be very difficult to implement, so hopefully this issue can be resolved quite quickly, or perhaps there's a better solution to this issue that I haven't come up with.

I don't agree with your view of the five latest technologies. I think they are decently balanced in comparison, for example, with the late game technologies in ES2, which were fairly situational and most non-scientist players would only get one of them in a playthrough. I do however agree that nuclear weapons might be accessible much earlier than the Devs have anticipated due to the structure of the contemporary era tech tree, especially when considering that the mechanic of mutually assured destruction is useless if only one side of the conflict has nuclear first strike capability. I also agree that making Wireless Telegraphy a requirement for the Research Insitute is a sensible fix for this issue (if it is one). I don't think the change to Fusion Reactor is necessary.

I read this and all I can think is that it will form the foundation for an excellent Spiffing Brit video

You talk about how things won't work as intended. Making some assumptions there. Bad habit. I suggest you break it. 

Now. Your big point: "It should have some techs as prerequisites". I say no. The way it works now this means a science heavy empire has similar access to nukes as one that isn't science heavy. MAD is critical to nukes not being OP (assuming they are worth using). If science focused civs get access much sooner because they can pound through a pile of techs faster then science focus becomes the meta. That nukes are just a couple techs into contemporary means as long as you aren't super behind on age progress you don't immediately lose to science people who get to swing world enders at you before you can MAD them.