I can walk into most any Home Depot and buy a few feet of oak. Would that not do the same thing?
Yes, it would. I've picked some up at H.D. for the same purpose.
As previously mentioned, basswood is popular because it's inexpensive and can be found in hobby supply stores, pre-cut to sizes that are ideal for a strop. It's sold for carving crafts like making wooden models, etc.. I originally used it for that convenience and it works fine for stropping.
Any wood that's cut to an appropriate size and is smoothly finished will work for strops. And woods with a very tight, dense grain are also good (basswood, poplar & maple, for example, all of which I've used at times). You might see over time, experimenting with different woods, that you'll favor a particular variety for your own specific reasons. Basswood works well in part because compounds applied to it will embed very well into the surface and it's also firm enough that it won't easily be compressed or dented under pressure from your blade. Softer woods like balsa are also popular for strops, but they're prone to that sort of compression damage and will be more needy for resurfacing over time to keep them flat and smooth. Oak is VERY HARD and can work well, but sometimes I've felt the grain is a little bit too open as compared to a tighter-grained wood like basswood or maple.
When the strop gets heavily loaded with metal swarf, it can easily be resurfaced by sanding or shaving a layer off the surface with a hand plane - that's my favorite method. Makes it completely smooth and clean again for reapplication of fresh compound.