The algorithm is actually pseudo-random though probably too hard for normal people to predict.
Randomness is kinda a false evil really. The randomness that is bad is randomness in match result. All other randomness is only bad insofar as it increases randomness in match result. Does Jigglypuff's Mystery Gift meaningfully increase the randomness of a match outcome? I don't think it does. If someone told me "I would have won if Jigglypuff didn't pull so many good items!" I'd just be really suspicious. For one, Mystery Gift isn't even that good so Jigglypuff won't use it all that often. For two, the main factor in Mystery Gift is that you just can't let Jigglypuff keep doing it. If you sit back and let her pull five consecutive items and she gets a pretty good one (a Pitfall or a Spring), well, who do you have to blame? Of course, in preventing her from making items, you perhaps expose yourself which is what Jigglypuff really wanted. The quasi-randomness ensures that you never *really* know how important stopping any given Mystery Gift is so you can't game the system and only try to stop the ones that would make good items.
Peach players will recognize this. Peach's Turnips work similarly, but it should be noted that as an overall move Peach's Turnips are a million times more powerful than Mystery Gift. They create really interesting gameplay in the balancing act of how you go about stopping her from pulling them, and the positive of that greatly outweighs any inherent negatives of the randomness. There's no way they could be predictable and have all their good effects on the game as well; the fact that every pull is a potential threat but that a large number of pulls is still only going to produce a small number of threats (but with increasing certainty of a threat at all) is what we are looking for here.
By my count, the following other moves are also random: Luigi's Green Missile, Peach's fsmash, Diddy's Rocket Barrels (if knocked off him, they travel with a random path), King Dedede's Waddle Dee Toss, Olimar's Pikmin Pluck, Mr. Game & Watch's Judgment Hammer. The majority of the stages in the game also have some random effect that is gameplay relevant: Delfino Plaza, Mario Circuit, Rumble Falls, Bridge of Eldin, Pirate Ship, Norfair, Frigate Orpheon, Yoshi's Island [Brawl], Halberd, Lylat Cruise, Pokemon Stadium 2, Spear Pillar, Port Town Aero Dive, WarioWare Inc., Distant Planet, Smashville, New Pork City, Skyworld?, Summit, 75m, Mario Bros., Flat Zone 2, PictoChat, Green Hill Zone, Jungle Japes, Onett, Corneria, Green Greens, Big Blue, Brinstar, and Pokemon Stadium 1. Some of the random effects are pretty small, but try me on any of them and I'll point them out! The amount of randomness already in the game should diminish our fear of randomness on principle.
I hope this explanation diminishes your concerns over what is honestly not a very significant mechanic for Jigglypuff.
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To answer a potentially dangerous but seemingly innocently intentioned question directly before it gets out of hand...
The short version is that Balanced Brawl has a very clear design philosophy toward which it strives in a careful, conservative way with a big focus on polish and preventing hurting what is good in the game. That is not a description of Brawl+, and that makes the projects just about fundamentally incomparable. Otherwise, it is probably not very productive to have a discussion over the merits (or lack thereof) of Brawl+ as this topic is not about Brawl+. I will give you my utmost confidence that Balanced Brawl is not only the most balanced of the assorted Brawl mods but also the most balanced Smash Bros game ever so if you are simply seeking balance, Balanced Brawl is indeed designed to cater to you. We are confident that all 36 characters are competitive and not only that but competitive across a broad spectrum of 28 stages leading to 36,288 interesting and deep match-ups for you to explore. I think that actually beats out not just all the other smash games but also every other fighting game ever.
