I use the tempo track, rather than just changing to a different fixed BPM in the transport bar. But this is mainly because different parts of my songs have different tempos. Otherwise, the one-button click would probably be what I chose.
And audio stretching for me is OK for self-demo purposes (i.e., to determine if the new tempo is the right one), but I’ll re-sing when I settle on the right tempo.
But … the main thing I do is try to avoid all the above stuff by endless practicing/rehearsing, even before recording, like I’m singing live in a small club, just me and my piano, until the right tempo declares itself over time. I might check it out with a scratch recording, but the main work of figuring out the “right” tempo has been done long before that. Only then do I do the real work of recording and subsequent steps. To me, the added benefit of doing it this way is that things like phrasing and such are so much better by the time I get to tape.
For me it quite often boils down to several distinct operations. First there’s the writing where I get creative, get a feel for what I want, record midi and record audio. Then there’s the arranging where I cut the ideas up, speed up, slow down, song length etc. Once I’ve settled on the arrangement and specifically the tempo(s) then I start recording. During this stage I’ll most likely replace everything that’s audio unless I have real trouble repeating the vibe. I’ll tidy up midi or improve it, and pick instruments. When it’s all recorded I switch to mixing, although I’m often mixing as I go along in a rough manner just to keep the vibe.
So, to answer your question, I keep the tempo flexible while writing the music and I fix the tempo when I’m finalising the arrangement. I’d start off by tapping a rough tempo or recording freehand, then I’d fill in the tempo map as I go along. If I’ve got audio at different/wrong speeds then I’ll use musical mode or time-stretching to create the arrangement on the basis that I’ll replace it later. I even use things like pitch shift on audio for instant key changes, sounds awful sometimes but it serves the arrangement and 'll be replaced later.