No good idle on restart of warm engine
 

So after an effortless start first thing and subsequent drive; I get to a destination, try to restart the car after a while of sitting it starts, fires up but fails to sustain an idle without throttle input.

in a few seconds, idle is sustained again?

2007 XK with 81K miles

Is my MAS failing?

Mine does that occasionally too.

Sounds like it's time to pull out the ODB reader and check the codes. There's a few things it could be and you should see if any are throwing codes. Crankshaft/Camshaft position sensors, a coil drawing high voltage, MAF, etc..

If the check engine light is on otherwise there will be no codes.

Fuel injectors are leaking

I SORT OF had a problem like this in my P/S Mustang; It'd start and run fine, but if I shut it down for more than five minutes it would barely crank over. If I waited more than 15 minutes it'd start fine.

The problem was that three of the four power valves (dual quads) were leaking fuel into the intake and going past any open intake valve and somewhat hydro-locking the engine. That made for some smelly oil, which is how I found the problem.

If it won't throw a code then the processor thinks it's running OK. Look at sensor inputs or wiring problems. A good OBDii reader will help a lot.

Look at OBD live data.

Check things like fuel trims, ECT, IAT and so on for anomalies.

Cost $5 up and some effort.

In addition, the day I took my car to the track, after running very hard on the track, I let the car sit for 20 minutes. Trying to start the car after 20 minutes was horrible. It sputtered, shook, and wouldn't stay running. Ultimately I could get it started and after revving and playing with the throttle got it to smooth out. Then I ran the track again, and after 20 minutes of sitting, same thing on re-start. Never got a check engine light.

Maybe as stated above, fuel injectors leak by and fill the engine with gasoline?