Americans seems like it is the weakest culture in the game relative to its era, in fact it is probably weaker than some ancient era ones such as Babylonians who have been transcending to contemporary. Lets compare the cultures:

Legacy traits: 

American Exceptionalism (Americans): +10 Influence on Resources being sold +1 Money generated from on-going Trade on City or Outpost 

Brilliant Philosophers (Babylonians): +2 Science per researched technologies on Capital

American legacy trait is really unreliable as it depend on other players actually purchasing your goods or allow you to trade with them and even in such case it is a pretty weak trait compared to what other contemporary cultures get. Also the american legacy trait will probably not work all that well with the expansionist affinity, sure you may be encouraged to control more territories and more resources, but on other hand it will not make you liked and may cause grievances that can lead to demands which can shut down your trade and thus you lose the bonuses from the legacy trait. 

Babylonian get a pretty weak legacy trait compared to what like Harappans or Egyptians get but atleast it always give you something. I don't think it is better than the american trait, I think I rather have american trait over babylonian (in a real game you can get both as they belong to two different eras), both traits are weak.

Emblematic unit:
Lightning (Americans): Replace multirole fighter with +3 strength and aerial stealth trait

Ṣābu Ša Qašti (Babylonian): Replace spearman +4 strength and gurdian trait but twice as expensive

Lightning is a weak upgrade on a strong generic unit. The aerial stealth trait is pretty much useless, all it do is to prevent attacked me grievance when you bomb units of a player you are not at war with. It don't work in any other situation such as when you bomb outpost, trade routes or anything else and neither do it allow you to bomb players you are at peace with inside their territory. Thus I think it is fair to just say that lightning is a multirole fighter with +3 strength, which is worse than soviet or germany generic multi roles as those have the same strength, but also a -20% cost reduction. In contemporary many emblematic units cost half as much as their generic counterpart and maybe also comes with more significant improvement and traits, only good thing about lightning is it don't come with a drawback (except you have to play as the americans).

Ṣābu Ša Qašti is an interesting unit, much more expensive but much more stronger than a spearman, especially when defending districts due to its guardian trait. This make babylonians tough to conquer early on given behind fortification this unit will have strength above 30 when defending against attack. On other hand its high price may limit its use and may be a drawback as you will have a harder time to field anti cavalry units, even if those are much better than the ones other cultures get.

Anyway since we are talking about contemporary, the Ṣābu Ša Qašti should be obsolete a long time ago, so again americans who actually have an contemporary emblematic unit that is straight up better than its generic conterpart, even if not the best version of it win over not having any emblematic unit in contemporary which is the case of babylonians.

Emblematic district:

Defense Agency (Americans)

• -10 Stability
• +2 Combat Strength in combat for Units in or adjacent to the District
• +2 Influence per adjacent Garrison

• -10 Stability
• +3 Science per adjacent Farmers Quarter
• On City or Outpost:
• +1 Food per Researchers
• +1 Science per Researchers
• +1 Researchers Slot
• Count as "Farmers Quarter"
• Count as "Research Quarter"
  

This time I have to give the win to babylonians, even though astronomy house is in ancient era, it is a far better district than defence agency and in fact is a good reason not to pick americans if you are the babylonians in industrial as if you do you lose the ability to build astronomy houses. The defence agency is so terrible you would probably not even build it, there are probably better ways to get more influence and in every other way it is inferior to the cheaper garrison.

Affinity:

Expansionist (Americans)

Scientist (Babylonians)

While expansionist can be nice, like being able to enter everyones territory allow you to keep armies near their cities for quick wars and conquest and the ability to take territory once every 15 turns or so have uses, it don't have anywhere near the impact of scientist affinity. Sure in contemporary, scientist no longer can research an era ahead, but they can still convert industry and money into science for a very fast tech rate and given you can get alot of fame and end the game with technology, I think scientist is the much stronger affinity in contemporary or even the whole game Also it is generally much easier to get the scientist era stars than it is to get the expansionist ones. Screenshot below show the impact of collective mind ability, don't think there is anything similar expansionist affinity can do:

Conclusion, if you are in a case in contemporary in which you can pick the americans or transcend as babylonians, I think you are probably better of staying as babylonians. Sure you get another legacy trait and an emblematic unit, but both are weak and transcending give you +10% more fame may very well be stronger than american legacy trait. If you pick americans you lose your great scientist affinity for the inferior expansionist affinity and you can no longer build astronomy houses if you still are building those, defence agency is so terrible that they will probably not be built at all.

I very much think americans need to be made more competetive and similar in strength to the other contemporary cultures, the defence agency is its main weakness but both the unit and trait could also be made better. Also the scientist affinity should be made less impactful, given it by itself can pretty much make a culture strong before we even consider the uniques of that culture.