i'm about 26 years into a 1900 start, and the AI has reverted to 9-inch gunned battlecruisers and 10-inch gunned battleships entirely because it couldn't keep up. and alongside scrapping any slightly aging design like it's going out of fashion, these have killed any further interest in my most recent US campaign.
i think a good solution when it comes to being unable to keep up with the techs needed for shared designs is for the AI to be able to consider more than just that year- if it's Japan in 1925, and doesn't meet the requirements of 1925 techs, it then falls back onto designs from as far back as 1920- kind of like a player building a ton of obsolete ships just to immediately refit them.
there further may be a need to limit the AI when this scenario eventually pops up in a long playthrough, like outright deprecating the use of 9/10/11-inch; and even later 12-inch; calibers on battleships once a tech like 14-inch II or 15-inch I has been researched.