Having used and favored basswood for most of my compounded stropping, I can say one would have to REALLY lean into it to actually raise a burr against this wood, if it's even possible to do so. It's firmer than balsa, but still 'soft' enough that it's virtually impossible to burr the edge or roll it, UNLESS one were using very coarse-grit compound, which might raise some noticeable burrs with moderate-to-heavy pressure applied. In that case, it's more about the grit than the substrate. But with the polishing-grade compounds I've used, including diamond in the 1 - 6µ range, and aluminum oxide in the 3 - 10µ range, I've never been able to raise a burr on a basswood strop, even when deliberately upping the pressure. The wood will sooner give way, by denting or gouging before the edge deflects, if anything.
Both balsa & basswood seem to do a lot better in giving compound a strong, more aggressive foothold, as compared to leather. The thing I noticed immediately, the first time I started using wood for stropping was, it removed metal a lot more aggressively (faster) than when I'd tried the same compounds on leather. The wood strops blacken up very fast in use, whereas the leather strops gradually 'gray' over some time, with use. That tells something about how the substrate helps the compound work.
The basswood I've used for stropping is thick enough, it's easy to completely remove the top layer of dirty swarf and expose clean, fresh wood underneath. Can be done by sanding it, or I've liked using a block plane to just 'shave' a thin layer from the top; that also leaves the surface very smooth & FLAT, and completely clean. This is a big advantage also, if you choose to re-purpose a given block for a different compound, and don't want to worry about the older compound contaminating the new strop. If not wanting to completely strip a layer away, it's also easy enough to just scrape the surface with something to take most of the heavy swarf off. I've sometimes done this with the burred edge of a metal paint scraper (like a putty knife, but wider). I used a file to burr the edge, in a similar manner a card scraper for wood-finishing is prepped with a burr. OR, as can be done with a leather strop, just wiping down the strop with a microfiber towel moistened with WD-40, mineral spirits or another similar solvent will remove most of the heavy black stuff, sufficient to make the surface take a new application of compound easily. There're lots of ways to clean these up, none of which are especially difficult.