Its not so much the depth of the head from my understanding, but the depth of the valve seats, as the heads get skimmed there is less metal holding them in and they become exposed and liable to fall out!

Compression ratio can be managed in a thinner than 138.6mm head by reducing piston height, thicker gasket etc

The other factor is softening of the aluminium of the head rather than the actual thickness, if its gone too soft the gasket beds into it and you also loose torque on the head bolts as a result.

As old decent heads become rarer then solutions will be found to refurbish them no doubt.

Also new castings are now available, costly but at least you can transfer all the guts of a damaged head into one of those and start again