The USFS [1] page on Paulownia tomentosa cites a lot of research suggesting that it’s a “transient” invader that rapidly settles harsh or disturbed (e.g. by fire) environments, but is highly shade intolerant and gets outcompetes in the long run. So it seems to me a good strategy is to use it to rapidly colonize non-forested areas, sequester that biomass, and eventually cultivate more diverse species (or something like that).

>”...thus, princesstree frequently establishes and spreads after disturbances that create these conditions, such as fire, windstorms, pestilence, floods, landslides, and anthropogenic disturbances such as construction, cultivation, mining, and logging”

> “Hu suggests that by the time Paulownia grows to maturity, the seeds it produces likely cannot survive within the same habitat as the parent plant because the succeeding vegetation has ‘modified the physical environment so much that no new Paulownia has any chance to get established’. Thus, princesstree may not alter the successional pathways of some native ecosystems.“

[1] https://www.fs.fed.us/database/feis/plants/tree/pautom/all.h...

The hybrid Empress Splendor tree is not invasive.

https://worldtree.info/empress-tree/

My question here, is, if this tree proposed a possible slice of solution to carbon capture, is it a "bad" thing if we let it spread over the world which would otherwise be hit by possibly run-away global warming?

From my perspective, and quoting interstellar "There's no time for caution"

I would go over and say that maybe even doing genetic altering of the tree, so it could fit our purposes better might be a good idea. Be it making it extremely vulnerable to specific herbicide or make it grow/capture carbon even faster

Given what we are doing about the climate crisis (nothing), I would be very happy to plant "highly invasive trees" and have them spread around like crazy. Too many of those trees is a much better problem to have than a cooked planet.