Yes I suppose, but the easiest SHFFLing can be done with the c-stick. By utilizing the c-stick one is able to control the attack and the jump movement at the same time. This alows one to space whilst performing an aerial. Basically the control stick to control the spacing and the fast fall aspect of SHFFLing; and the c-stick to determine the timing and which aerial to use. I'm sure it's perfectly doable with an arcade stick, (and yes, there are pro's who can space and SHFFL without the cstick, though far and few between), but the OG Gamecube mapping has proven very compatible with Smash Melee.
The problem with your argument is that there is no spacing available at all. Just straight out SHFFLing. There is certainly more to it than that for performing aerial attacks or SHFFLs. It is possible to space, but the input of commands will be significantly strenuous on the person (requires much much faster inputs). WIth the Gamecube layout, you can do two things at essentially the same time, instead of things one after the other).
I dunno, I'd rather do two things at once than perform those two seperately under the same amount of time.
Oh, and not everyone is versed well in fighting terminology. When they see 236+p for the first time, I guarantee the person will not get what one just said. But in smash where a simple "press b" or "down b" is all that it takes to teach someone the basics of the game... That's what makes Smash one of the easier fighters (if you wish to consider it a "fighter") to pick up. The way of memorizing moves via mortal kombat hotline and going to the local arcade to show your technical prowess is long gone. People exposed to new games, generally want ease of use when picking it up. I'm sure someone new to a game doesn't want to be bombarded with 236k, sj, 623hs, frc, d, ad, 6hs, iad, d.