That's odd though because I am going through the effects, and they don't seem to quite work like that. Rather, it probably does, but it's not quite like you'd expect.
The options in the first dropdown tab of BrawlWall have effect values of 0-11 (they're listed in order in BrawlWall). They also all correspond to sound effects from stepping on said ground (let's ignore 0 which is "none"), though some have low friction labels so perhaps the sound effect and the friction are tied together. The only hex values in this range that are of the 2^n are 1, 2, 4, 8, and 10. It's my suspicion that values less than 20 are all treated independently and that beyond that you have the combination model.
In hex, the four options in the second window are 100 (DropPlatform), 2000 (GrabLeft), 4000 (GrabRight), and 8000 (NoWallJump). This leaves 200, 400, 800, and 1000 unknown but presumably independent. The fate of 20, 40, and 80 is very unclear; they could be treated as part of the general "hardcoded combination" set, or they could be independent. Values over 8000, if they exist, are presumably independent.
I'll now document everything I can find which is currently unknown.
12: Used for one piece of ground near bottom of Target Test 3, also on a right wall nearby and two roofs (were these spikes?), also one piece of ground on Target Test 5 (pretty sure it's spikes)
15: Hanenbow (throughout)
18: Luigi's Mansion outdoor ground/rooftop, Rumble Falls assorted ground, Mushroomy Kingdom ground, Bridge of Eldin ground, Spear Pillar upper part ground/platforms, Castle Siege form 2 (not "tarps" but everything else), Skyworld ("solid" ground), Target Test 5 ground
1A: Mario Bros. lower ground
1B: Delfino Plaza floating platform ground, Mushroomy Kingdom Pipe tops, Pokemon Stadium 2 flying form ground, Port Town Aero Dive ground (not clear where, not universal)
1C: Delfino Plaza sand ground
1D: Homerun Contest Arena ground
400: one small piece on the bottom-left corner of Pirate Ship, Frigate Orpheon everything except PT's platform, Pokemon Stadium 2 ground form dirt mount, PictoChat drawing 9, Shadow Moses Island tops of walls, Big Blue Falcon Flier (used in combination with other values), walls/roofs on tree in Pokemon Stadium 1 fire form, walls on rock form Pokemon Stadium 1, windmill on water form Pokemon Stadium 1
916: Summit clouds, Skyworld clouds
Stages checked: Battlefield, Final Destination, Delfino Plaza, Luigi's Mansion, Mushroomy Kingdom (both), Mario Circuit, Rumble Falls, Bridge of Eldin, Pirate Ship, Norfair, Frigate Orpheon, Yoshi's Island (Brawl), Halberd, Lylat Cruise, Pokemon Stadium 2, Spear Pillar (only checked STGTENGEN_1.pac, other two should be identical), Port Town Aero Dive, Castle Siege, WarioWare Inc., Distant Planet, Smashville, New Pork City, Summit, Skyworld (not 100% thorough), 75m, Mario Bros., Flat Zone 2, PictoChat, Hanenbow, Shadow Moses Island, Green Hill Zone, Temple, Yoshi's Island (Melee), Jungle Japes, Onett, Corneria, Green Greens, Big Blue (didn't bother checking every individual car), Brinstar, Pokemon Stadium 1, WiFi Training Room, All Star/Boss Battles Rest Area, Homerun Contest Arena, Configtest, Results, Target Test 1-5
That's really enough for now. 18 is obviously a common sound effect that was just missed. I'm betting that all the other low values are just uncommon sound effects.
I legitimately have no idea what 400 could be. I don't know which drawing PictoChat's 9th one is; the image is way too confusing to figure it out. I just can't imagine what's special about the Falcon Flier... I really don't know, but I should point out that it is used on all pieces of the Falcon Flier, including the walls and underside. The game typically doesn't use effects when they don't do anything. Pokemon Stadium 2's odd inclusion here doesn't exactly shed light on the subject. The Pirate Ship case is even more baffling!
916 seems special because it's such a weird number, but I think I can break it down. 16 is probably just another unique sound effect, and 100 is known to be DropPlatform. That leaves us with 800 which I'm willing to bet is the property that lets you hit people down through the clouds on Skyworld.
We know of sound effects up existing up to 1D now; if I were to hazard a guess, I'd guess that 13, 14, 17, and 19 all exist but just haven't been found yet, either on Rainbow Cruise or Subspace only (and probably more beyond that, but I have no idea what the limit might be). Given the massive number of stage files when subspace stages are factored in, there's really plenty of room for these.
As per the interesting values (the sound effect things only seem to matter gameplay wise when it comes to friction... not wholly unimportant but a fairly small point overall), I still haven't found any sign of the potentially mysterious or potentially just unused 20, 40, and 80. Among values far more likely to exist, I haven't seen 200 or 1000 anywhere; they must be confined to Rainbow Cruise and Subspace.
On another note, Mario Bros. has the most bizarre set of collision files you'll ever find. There seem to be only one object/plane in the whole thing and a whole lot of individual points.
I'm likely to update this post later as I search through more stages. I hope to at least end up looking through every stage in the melee folder (granted, BrawlWall not being able to open Rainbow Cruise is a detriment to that). I am likely only to look at stages in the adventure folder that I have some reasonable basis to suspect are going to be interesting; there are just way too many of them, and they don't matter much for the part of the game that is actually fun.
EDIT note: Homerun Contest Arena's breakable walls have an undocumented type value that seems to be 20. Figuring out what Unknown1 and Unknown2 do in general would probably be important for working out the type field fully.
I do have a suspicion about Unknown1 and Unknown2. In general, everything seems to have Unknown1 except things that only the Pokemon Trainer can stand on. So I think Unknown1 is "solid" in general while Unknown2 is "solid only to the Pokemon Trainer". For those unaware, the type values go like this:
0: None
1: Ground
2: Roof
4: RightWall
8: LeftWall
10: Unknown1 (I suspect "solid")
20: Undocumented (only used for breakable walls on HRC)
40: Unknown2 (seems to only be used for PT platforms that have no interaction with normal characters).