It seems every music shop & warehouse stores drums this way, I see no issues with it other than one may have to re-tension the heads when it comes time to setting them up again--which you'd do anyway. Stacked drums take up the least amount of floor space.
I cut a 2' square of 1/4" plywood to set on my bass, then stack the rest on top of that---seems fine. The weight ends up being on the T's, both lower & upper ones evenly, which probably compresses the springs in the bass lugs a bit. The weight gets spread out to 16 or 20 springs, depending on if it's a 20 or a 22. I only have 4-piece kits, & usually keep the snares on a shelf, so not much weight, overall. 1x2's are fine, too, I'm sure, but concentrates the weight to 4 spots on the wood hoop.....marko
I'm a stacker from way back.... My only concern is putting too much weight on the bass head inturn putting too much tension on the lugs and causing deflection/ warping of a thin shell. I stack no more than 2 drums on the bass. Probably not really going to happen. I've only seen this where the drums were tensioned really super tight over long periods of time.....ok I'll shut up now
If you look at it purely from a structural standpoint there is nothing wrong with stacking drums.
The head will resist equal tension and put the shell into pure compression. A circle/arch in compression is about as pure economic a structure as you can get. Plus the pipe shape of drums is also a very economical structure when used on end. Take care not to mark your heads up and all will be well. Another critical point is where the bottom shell touches the ground, depending on how high you stack ideally that force should be distributed to as many points as possible and kept off the tees.
One of the music shops I frequent stack their kits with the bass drum set up. Floor tom with legs on top and then toms and maybe a snare. I think 2 of the FT legs are resting on the bass lugs or t-rods and the other one on the shell. I've never tried it and don't think I would, but it can be done.
How about cutting out squares from a thin, stiff sheet of plastic which you could insert between each of the stacked drums? It would at least keep the final height & weight down as opposed to using 2x4's.
I have been known to sit on drum heads to seat them. Plus you do remember that we beat on them with sticks, right? Stacking drums won't hurt them and may actually be better for the bass than leaving it set up with toms mounted on them.