you can just make a little change on the rule for generating new accounst to achieve your idea: choose a specified string and make a dural encryption on the string, let it be your secret key, generate a public key for it as your btc account, then you only need to remember your specified string and do not need to keep any wallet.

while the bad thing for this method is that even others are not able to decrypt your account. It might be easy for them to guess your string, because your string should be simple enough to be memarized. if you want to make it safe from being guess out then it will be hard to remember even for yourself, so you need a note somewhere to write down the string, and that's your current wallet.