Engine failure

I had a situation yesterday at the end of my local "just because" flight
(you know, one of those where you really have no place to go but the weather
is favourable and you just want to go flying).

Was flying a rental 172. Took off like a rocket (lightly loaded solo...
cold air about freezing), tooled around practicing stalls, steep turns, etc.
Headed back to the pattern and did a couple of touch and goes. On my final
landing, I declared a full stop, and decided I would practice a short field
landing. I cleared the "imaginary" 50 ft. obstacle, dropped the last notch
of flaps and cut power... and the engine quit. No issues, because I had the
runway made (I didn't even realize that the engine had quit until rolling on
the runway... I knew something sounded different, but the prop was still
windmilling and I was concentrating on the flare).

I rolled out and the prop stopped, and I called traffic (uncontrolled
airport) to let them know I was a sitting duck. Checked the primer
(locked), mixture (full rich), fuel selector (both... and lots of fuel... I
filled up with only just over an hour of flight since), and restarted with
no problems and taxied off the runway.

Though it turned out to be no danger, I couldn't help but feel a little
disconcerted. A low level power off descent away from the airport could
have had a more serious outcome, or what if I misjudged and didn't have the
runway made when I cut power?

I taxied to the maintenance hanger (after being directed there by the FBO
via radio notification of the situation), and explained what happened to the
maintenance guy. He said that there is a stop on the throttle to keep the
idle setting from being too low that probably needed adjustment. Even so,
during shutdown (after restarting), idle setting on the throttle was still
800 - 900 RPM, which should be enough to keep the engine running I would
think.

Anyone else experienced this and can share their thoughts? I'm about a 60
hour pilot, so not much experience.