Good questions. I'm far from the expert that Elaine is, but;Whats the problem that lime and gypsum is exacerbate? And how do you till in the compost when you aren't doing any tillage? Also if the indigenous biology knows how to deal with it why would add any in compost?
In this context it's assumed that lime/gypsum will help clay based soils flocculate and improve structure - other people decide to lean on it to do other things, such as supply calcium into a system that sells calcium out the gate, or to "sweeten" soil that's being degraded by being hungry
Locally, you see a lot of this - clearing bush off land and then killing off the native biology/mycorrhizae by using tillage and brassicas (non-mycorrhizal hosts) and then rebooting the system with new grass species and fertiliser (because the mycorrizae are no longer there to feed the pasture, hence the bright yellow + p!ss patch appearance)
In this relatively inert substrate, it could be more beneficial to till in compost than simply leave it on the surface to blow away, anything that could have helped the process has largely been killed off anyway.
We just "sheet compost" by wasting a heap of grass early in the season and letting the soil do what soil does.
It's contextual, we have a much different context to if we were, say, trying to get plants reestablished on an old quarry or floodbank that is bare soil. That biology is going to starve quickly without a food source (plant exudates and litter) so compost is the quick way to deliver dinner.