Well, we know that Firaxis is monitoring the forums, the same with reddit, so the discussion is relevant also for Firaxis. However, I think they do not look so much on how many people bring forth an argument how loud and how many times, but instead if the arguments hold.
The conflict I see on this one is with MP, as mentioned before. If Civ 6 would have been Age of Empires, Babylon would have been nerfed already.
I do not want Babylon basic mechanic to be nerfed, since I think its fun. XD
I loved AoE and played it mainly in MP. I love Civ 6 at least as much, but never play MP. That is why I enjoy it as it is.
IMHO fixing Babylon for MP is very hard. A Civ picker is the quickest solution here. But maybe there is another approach (see below).
Here's an idea: Inspirations only boost 25%. If all Inspirations in an Era are triggered, immediately boost an additional 25% to all researchable Civics in that Era.
I like the idea, but I think something like this might a thing for another, new civ. I like the simplicity of the approach of Babylon.
Tech eurekas are usually depending on gold/production
The only way Babylon could maybe nerfed is as a side of effect of reviewing the eurekas: If a tech can be eureka'd by building something that is only available due to having another tech, this makes the eureka only depending on either gold/production (buying/producing the unit/building required for the tech) or great person points (e.g. a great engineer to fast produce a wonder). Since we can blitz to industrial zones by building 3 mines, we have a more production with Babylon early.
Suggestion: Check, which critical eurekas could be changed to depend on the civic tree
But whenever we have dependency to the Civic tree, the blitzing is prevented. So maybe there are one or two eurekas which could effectivly be tied to the Civic tree to
a) slow down Babylon
b) but which would also make more sense for all Civs and improve the worth of Civic tree.
Possible techs to change: Metal Casting & Castles => We do not even need more dependencies on the civic tree!
I would suggest to change the eureka for Metal Casting. Currently its eureka is "Own 2 crossbows". This is a boring eureka, since it is essentially the same as the eureka for Machinery, which is "Own 3 archers". It's just a little bit more expensive to get (500 gold in upgrades to archers compared to 180 gold for upgrade 3 Slingers to Archers - without "Professional Army" policy, of course).
The most appealing alternative eureka for Metal Casting IMHO would be to swap it with the eureka for Castles, which is "Adopt Government with 6 inherent policy Slots": The Castles tech does not give very powerful things (Medieval Walls, Coursers, ...) and owning "2 crossbows" is complementary, even most of the times you get the eureka for a tech by doing a thing from a previous era. Well, Castles tech is medieval, and so is machinery, but "6 policy slot government" is also medieval: Monarchy (from Divine Right). You might say, that eurekas should somehow make sense from a story telling perspective. Well for these two techs IMO the swapping does not hurt: 2 crossbows do not make a bombard, and a complex government does not make a Courser -> the eurekas are currently not very meaningful, so we can also swap them around.
That single change would both prevent super early Pike&Shot, Bombards, and therefore Field Cannons (you can see this for my "dependency process graph", or whatever you want to call it, above). You would need to invest a lot more in culture to get to that, and it would delay getting to these units in a senseful way, which I would like.
New patch makes some eurekas easier to get
This is something a little bit disturbing in the light of the current discussion, since both the eureka for Industrialization and Refining have been nerfed in the next patch. Now you only need 2 workshops for Industrialization and 1 Coal Power Plant for Refining. This makes battleships easier to get for Babylon. Still, all of the stuff is expensive to build or buy, but I would not have asked for this change.
But since we do not have the patch, yet, we still need to playtest how it feels. Maybe other things have been changed, complementarily, and this is just fine.
Still, the change to Metal Casting would be something really effective, while being very simple, the more I think about it. No big change for anyone, but an effective blocker for Babylon while keeping its simplicity of its basic mechanic, which I like so much.
Edit: To be on the very defensive safe side, you could change the Metal Casting eureka also to "Have an military alliance", but I think this is too hard to get...