Another truth often forgotten: the recipient's phone remembers everything, too. You might use full-disk encryption on your phone, but that doesn't matter if the recipient doesn't.
Your local data retention laws and the network's practices may vary or they may be under pressure from law enforcement to keep things longer than necessary. They will not disclose in public how long they are stored, so better assume forever.
Disclaimer: Statement obviously does not apply outside of Canada, US, UK, etc.
Side effect: may reduce information overload or search time for important messages. Unproven. Just a guess.
The only issue is in pretending this removes the message from the other side (like Telegram). Bury it in advanced options, put up a big warning or whatever. But to say people will get too confused and think it magically deletes other people's data ... that's a poor deal for serious users.
As-is, Signal users must diligently wipe information in case they are, for instance, stopped by police. Or in any other situation where they might be deprived of access for a bit, then be compelled to open the device. Perhaps they were in the middle of talking to someone. With a 1-5 minute timer, Signal can be useful enough to chat, while not risking too much if it's forcefully removed from you.
It's also just good hygiene in general. Most people are probably better off having old data get wiped automatically some time later. Opt in to perma-save. It's not comprehensive, but it sure helps users avoid an accidental disclosure.
And no, length limits are not good enough since they span an arbitrary amount of data and time. In fact, I'm not even sure of the point, unless it's to speed up the UI or something.