I am researching quite a bit on native land management and perhaps it is all futile. Nature likely knows best. Probably the best thing for nature is to get rid of the human introduced species of humans
Native Americans it seems did manage their land though--in ways that would promote the biodiversity that favored them. I need to find the article, but when they brought a Native American chief to yellowstone after they had taken the land away from native americans to make national parks--he claimed that it looked unkept and messy.
Perhaps many of the species that we consider native are a result of human influence either way. It is true that many Native Americans tribes had done land management for years in the form of controlled burns, and they themselves selectively bred species such as the sunflower to yield what they wanted. Controlled burns are still used for prairies. It seems that in order to keep biodiversity, well-meaning humans are keeping lands eternally in a specific stage. Since there is less land overall, it makes since. As things like prairies and burned forest would be first to be developed. Like you mentioned trees that come just after a fire or other pioneer plants will be gone shortly as the land progresses to it's next stage.
I would argue native is better than just any tree. I think it would also give birds, used to foraging for native plants, an advantage over invasives. I've noticed the suet blocks I put out attract primarily starlings. However, I've seen cardinals, bluejays, and mourning doves on the native tree in the back.
I also watched this film yesterday, which was a nice respite after seaspiracy which left me with dread.
https://www.youtube.com/watch?v=3VZSJKbzyMc&t=20s
Notice he let the weeds in specifically to advantage the growth of native trees. I sometimes wonder if digging up my sod, solarizing my lawn, adding woodchips--is even worth it, or if nature would find a way even with the invasives. Probably not, given the tiny size and the use of herbicides/pesticides all around me. It is interesting as the first year I left my lawn to do what it wanted, it was large, taproot type of weeds like wild lettuce and of course dandelions, now it is ground cover with, wood sorrel, and creeping charlie, field madder and vetches.
I remember reading a permie account of solarizing your lawn with cardboard and woodchips without mowing, and planting sunflowers the next year. It's ingenious because the sunflowers would dig through the carboard and deep into the soil underneath, bring nutrient's from the decomposed wood. But what I found really interesting, is that nature itself did this with my lawn without me having a hand in it--with taproots the first year without pesticides, and then an abundance of plant variety the next year--invasive or not.
This year (the third under my watch) was the first year that natives came to my lawn without being introduce--prairie wildflowers like tenpetal anemone, sweetclover, and a type of vervain. I set up a patch of naturalized/native wildflowers, another patch of wood chips, am mowing part of the lawn, and letting the rest do what it will.
All of that is to say, I do not know if human involvement at all is beneficial in any way besides for humans, and if any involvement comes at a cost, marginal or not, to the environment. Perhaps even the Native American management was not sustainable once the population would have reached a certain level, it may have been simply a case of a small population. Who is to know? When I dig up and solarize my lawn, am I reducing nectar, cover, and material that animals would have used, invasive or not--for a season for no good reason? Would natives have sprung up eventually anyways? Perhaps invasives only thrive because we have a hand in it--like trying to feed native birds with manufactured suet or trying to keep land as perpetual prairie when it really should develop into brush and beyond.