My experience is to mulch it, seed it and keep it maintained. I've got areas on my property that I mulched down over 20 years ago and I've never had any stump issues. Most were hardwoods with some pines and cedars mixed in. No holes to be found. I normally mulch anything in my path up to 20" dbh but take out larger stuff when required to.
Mulching out nothing but the small weed trees and then calling in an excavator would be inefficient in my experience. If stumps need to be removed, doing it after mulching them down to grade will speed things up as they will break apart easily with a Tiger Tooth mounted on a bucket corner. Even when dozing, low cut stumps will break apart easy. The excavated stump pieces can then be mulched and a finish cut put onto the project prior to seeding.
Holes may be an issue with soil type as the soils get wet and then dry out in cycles. As a stump rots, I would expect the soils that were disturbed by the growing stump would naturally be inclined, by gravity and water, to settle back down into the original positions.
I've had a number of farmers and property owners that have seeded property after I've mulched it and never had any complaints about stump holes. This has been through a variety of soil types from MS River Loams to Red Rock Gravels, Flint gravels and Red Sand clays. The only problem I usually see is soil compaction around stumps which makes them seem to raise up out of the ground and become a mower hazard.