The only reason scores even need to be deathless is in game where they're cumulative; you could bop an enemy for 100, get a 1-up, die, bop the same enemy on your next life for 100 more and just rack up the points while never running out of lives.
Conversely, times must be cumulative through respawns, at least for whatever time it took to get to the check you're spawning from. You could hit the last checkpoint in a Sonic 2 level, then wait until time over and you'd respawn from the check with 0:00 on the clock. That certainly doesn't count. If you just die, instead of getting a time over, the clock still reads what it did when you got there (at least within a second) and you're allowed to continue from that.
I remember a time when the Cosmic Wall rings strat involved a death: you would intentionally tank at check 4 so that you could respawn there and hit 5, 6, 2, and 1 for bonuses before returning to start with all the level's rings available to you. (That was before forward rail 1 skip made it unnecessary.)
