And that is exactly how playing against the bots in Live used to work...But of course since it wasn't broken, chess.com decided to fix it. Sigh.
AI personalities
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There are some workarounds listed here though...
https://www.chess.com/forum/view/for-beginners/where-are-the-rated-bots
Some of the AIs play as if they are a stronger human trying to give a beginner a good challenge, and then it is probably wrong to try to assign them a fixed rating.
It may not make sense to assign a fixed rating to the bot, if it is going to flex its strength to match your strength in some way.
Then what we need is some metrics to tell us what strength it is trying to play at, in relation to our own effort.
In other words, it might be nicer to add more transparency to how the bot is picking its moves.
How much is random? How much is to try to challenge us, but not overwhelm us? How much is to reward us and get the game over with if we played better than usual already? It might be possible to answer in terms of ratings.
For example maybe the engineers decided the Beth Harmon bot should play at maximum rating 1200, or the opponent's rating minus 200, or adapt the strength as the game progresses. The adaptive bots that adapt to the game are one thing ... it depends on the AI bot what could be said about the rating of its strength in a particular game.
It would be neat if the AI personalities' ratings were from games played. You would need to figure out some rules that work to prevent foolishness (eg only affect AI's rating if opponent was within +- 200 of AI's current rating, and count aborted games as won or something), but having their 'true' ratings based off who they have played would be much better than guesstimated ratings that appear to be off (maybe upped, seems like they play below their given number by a good bit but its hard to tell).