It's your option- but why I don't
1) at 3/days per move playing to mate from a "won" position could take months to even a year to finish. This is especially true if the losing player adopts the "dead man defense", i.e. maxing out time per move and vacation to effectively hope your opponent gives up.
2) I am interested in the quality of play, playing out a trivial position doesn't interest me.
3) Unless it's unusual playing a mate isn't all that exciting.
4) Since I am interested more in developing my playing strength - defending a hopeless position over multiple months holds little appeal to me.
5) Personally, playing on in the hope that my opponent times out in a won position strikes me as distasteful, particularly if it is a casual game.
6) Conditional moves don't help if the position is complex enough. Maybe the OP means s/he will play out mate in 3's but when I consider a position losing is rarely at the point I see mate.
I don't fault other people for playing out a game, in OTB typically vs non-masters I will typically play until they demonstrate they clearly can win.
When I am the one whose losing:
- I want that person to prove the win.
- I might win/draw on time
When I am the winner:
- Checkmate is more satisfactory than resignation and win on time.
- If you don't want to play it out there's conditional moves.