Lemmy doesn’t, since it’s not part of the protocol, and in both situations you still lose your actual id.
In general, there’s technical reasons why ids and instances are associated on Lemmy / Mastodon, but not UX reasons.
99% of users just want a username, i.e. @bigCommieMouth, they don’t necessarily want their identity tied together with the server they use to interact with the network, i.e. @bigCommieMouth, and if they did really love a specific server and wanted their identity tied to it, they could always just make @bigCommieMouth_kolektiva_socia.