Exodus for example, I dont think they collect your info. Let's say a government wanted to give a warrant for them to look into some random dudes wallet. Would they hand the info over or something or what?
If something like this happens, I believe Exodus will hand over only your wallet transaction history since they don't collect the emails, personal questions or any form of information during sign up.
Since the owner of the wallet is the only one with access to the wallet private key. If the government is lucky enough to get the owner of the account, he only can give the out the private key.