Legal territory should be calculated based on the peak period territory, otherwise why should Rome calculate based on the Mediterranean, Britain, and even Mesopotamia, India calculate based on the entire South Asian Peninsula and Myanmar, and China calculate based on the remaining territory of the declining period?
Because the hegemony of Rome does not exist, and is expected to continue not existing, and the hegemony of China does exist and is expected to continue existing, despite hiccups.
The balance of mechanics is based on what not only the players, but the AI, are able to do with them. One of the core mechanics of the game is the casus belli system for giving a basis for going to war. One of these, in turn, is the de jure ('legal territory' as your refer to it) casus belli, which over the course of the game goes from 'one county at a time' to 'all de jure territory at once.' If you make the de jure hegemony the map of peak period territory, you give every Chinese hegemon title holder a permanent de jure casus belli on the de jure territory until it drifts into another hegemony.
Which is impossible, since there are no other hegemonies for it to drift into. As such, de jure casus belli are an always-available casus belli for the hegemony of China for every part of the de jure hegemony scope.
Note that Rome, specifically, does not have this de jure option. The Roman Empire is de jure the territory that is held by the empire re-creating Rome. It unifies all the held de jure empires- it does not give a single de jure claim elsewhere.
What the Roman Empire does give is a 'restore imperial province' casus belli, which is not (and generally worse than) the de jure casus belli... not least because by the time you can use it, you very likely have either (a) already taken the territories, or (b) have considerably better casus belli than a single-duchy-at-a-time war. (Like, say, claimants for the Kingdoms.) This comes far later, and would be far less useful, than a hegemony-level de jure option.
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