Forcing all players to progress to the next age at the same time is absolutely necessary to prevent players from rushing to reach the end of an age in order to make sure they can play the civ they want to play.
Regarding crises, if it were up to me, I would do it a different way. I'd introduce crisis metrics, which are costs you incur as you do all of the things you feel will progress your empire. Each age would have its own unique set of crisis metrics. A crisis metric can be local, meaning each player will have an associated "bucket" that only that player's actions can fill, or it can be global, meaning all players contribute to it. As a crisis bucket fills up, the player feels negative effects. The magnitude of said effects grows non-linearly, where the player is barely affected at the beginning (but is aware that the meter is filling up), but as the meter fills up, things get worse more and more quickly. After a certain point, the player enters "crisis" mode, where they feel "explosive" effects that aren't just continuations of what happened before crisis. In crisis mode, the player is also be given a special set of tools (e.g. policies) to deal with the crisis, similar to how it looks like it's being implemented for Civ 7.
This would make it so that you're not always guaranteed to enter a crisis at the end of an age, and you'll have a choice to make between a) progressing your empire to its maximum potential and ending up in a long, uncontrollable crisis that ends up undoing a lot of that progress by the end of the era when all crises resolve automatically, and b) carefully balancing progress and crisis metrics trying to avoid or delay a crisis for as long as you can. I'd balance the game so that a) would generally be closer to the optimum than b) is, so most playthroughs will end up in crises, but at least this way, crises won't feel quite as forced.
Civ 6 actually has a couple elements that are similar to this. Loyalty (or disloyalty) is a local crisis metric, which leads to yield penalties in the early stages, and in "crisis mode" leads to rebellions. CO2 emission is a global crisis metric, which lead to natural disasters that are increasingly devastating. Unfortunately, neither feature really belonged in Civ 6. Usually, they were both too weak to be relevant (especially CO2 emission), and I think up until now, Firaxis was really hesitant to introduce mechanisms in the game that would grossly regress the player's empire.