Why is using a single phase device across phases of a 3 phase outlet OK?
Any cross phase wiring of a WYE connection will yield sqrt(3)* higher voltage. You have shown this in your simulation.  This can also be determined via phasor analysis.

The current flow in these phases will no longer be balanced, which may or may not be a concern.

As you note the motor will be running at 208V instead of it's designed 220 (which BTW is actually 110 @ 0degrees and 110 at 180 degrees).  This motor is designed to take two active phases so insulation issues should be safe.

Yes, you are right.