That's a neat trick, but not as neat as Signal's "sure, here's all the data we have - the time and ip address of their last use."
(I'm sure a bunch of the "better UX, UI, and features" people like in Telegram rely on them storing more data on their servers, so that comes down to a privacy/convenience tradeoff, which as others have pointed out almost always comes down on the convenience side for 99.99% of people...)
https://arstechnica.com/tech-policy/2016/10/fbi-demands-sign...