Well, That was fun. ...

Do I feel bad winning a 10 minute game on time with
 0.6 seconds on my clock?

No.

Should I?

Hell no.

I've lost games with winning positions because I ran out of time.   I win games where I'm in a recoverable position because they ran out of time.

I ** tend to ** resign a thoroughly lost position IF the opponent exhibits some sign that they're not going to blunder a back rank mate by not giving their king luft.

But at this <1,000 level of chess we all suck and, as GM Ben Finegold says:  You lose 100% of the games you resign.  120% of the games if you're Mike Kummer.  Terrible.  (1)

Here's a song with a chess board featured.  The chess board gets smashed with an axe.  A young Peter Dinkelage is, I think, in the video as well.

Robert Fripp / Andy Summers - A Chess Board is Involved

And, because I'm a giver:

A Better Fripp/Summers Song, No Chess, Hilariously Dated Video

(1)  GM Ben Finegold never said that.  Very suspicious.