Yes you can leave the stumps. I would try to cut them as flush to the ground as possible. They will rot out with time, and they will rot faster if you keep them moist and covered with mulch. The rotting stumps and roots will add organic matter to the soil which holds moisture and nurtures the root systems of your future trees. You can plant new plantings, such as trees and shrubs in between the stumps. Even lawn does reasonably well right up to the stumps, and will overtake them with time as they rot.

If you saw my front garden, you would have no idea it was planted amongst the large root systems of both oaks and pines that the previous owner had removed in that area (and ground down). Most of the oak still hasn't rotted much!

Or you could have them ground out.

on my 5 acres.. i do it all the time ...i am rather cheap and thrifty ... i just dont need that specific spot as an urban gardener might ...

if you want to plant other things.. just dig in between the stumps ...

you will probably have a magnificent mushroom show for the next decade or two.. as the wood underground rots.. enjoy the show.. its free ...

the prior owner violated the number on rule of gardening.. he planted a monoculture... and when one failed.. down went them all

if you want to do the same thing.. use a multitude of plants from diverse families ... some tree.. some conifers.. some shrubs.. etc ... you really dont need a solid wall for a sight block

ken

The better question is why pay to grind them out? Lack of space or extra money in your pocket.