I think its the whole "giant slowly awakes and regains their power" thing. Regigigas wakes up from slumber and takes a bit before it regains its full power. Having it as an ability /is/ kinda silly, kinda implies its always waking from a slumber, but abilities was the closest thing they had to represent that.
I think a modern gigas would have a different ability and just have the "waking up" thing be a unique boss battle mechanic (see eternamax).
To be fair I think modern Regigigas would instead have an ability where the first time you send it out it falls asleep. Sleep is 1-3 turns now, so it’s way more balanced for this sort of situation even if it’s a little RNG-y. To circumvent it further you could instead automatically use Rest the first time it’s sent out in a battle — this ensure 2-turn sleep and heals off hazard damage — but obviously Rest also existed when it was introduced with the same mechanics.
Any of these mechanics are a little strange in the ability role, as you noted though. Regigigas having the slow start / wake up only makes sense in the boss battle, after which point it’s awake and you own it and it’s already battled. I think the mentality back then was Regigigas is so hard to obtain it’s basically just a trophy and not really intended to be used in battle. It wouldn’t surprise me if at some point Regigigas gets a Hidden Ability, especially if we get another batch of minor Regis, and have it be spotlit a bit. If Gen 4 remakes were actually made by Game Freak, I suspect it would have happened in them.
As a side note, something I appreciate about the original Regi trio is how they did actually feel quite special on account of being single-typed Pokémon of types that on their introduction barely had any single-typed representation. In Gen I there were actually 0 mono Rock- or Ice-Type Pokémon, and of course Steel-Type didn’t exist yet, but in Gen 2 no mono Steel-Type or Ice-Type Pokémon were introduced either and the only mono Rock was Sudowoodo. Gen 3 gave us other monos for each type, in the subpar Mawile, Nosepass, and Snorunt and Glalie, meaning that the Regis stood out as the only particularly strong representatives for JUST their assigned type with no dual types. When you think through the type chart as a whole, they’re actually the best 3 types to be used for this, and I think it was a very intentional decision. You may be thinking what about Dragon-Type, but Dratini, Dragonair, Bagon, and Shelgon outnumber the other types, even if they’re not fully-evolved.
Of course, later on Regigigas eschews it as mono-Normal is very common, but a Normal-Type legendary is so rare that it gets a free pass IMO. Arceus is the only other mono-Normal legendary and its entire purpose is to change to any type.
Regidrago and Regieleki? Yeah, not so much. I actually think Regidrago does decent here — mono-Dragon FE Pokémon are not common at all, the only ones being Haxorus, Druddigon, and Goodra, and since it’s so late in the series this is now a better metric to work with. Mono-Electric is very common though with decently strong FEs, and there are plenty of types that fit the bill way better. Mono Bug has few actual FE and battle-ready Pokémon, with Pinsir and Accelgor being the best on offer. Mono-Poison actually has a great claim to this, because it is extraordinarily rare nowadays as a monotype; the LC Pokémon Poipole is the most recent one, before that you have Trubbish and Garbodor, and before that Seviper, Gulpin and Swalot! And, of course, Mono-Flying, but Tornadus sort of occupies the “this legend is cool because it’s mono-flying” territory already. I think Poison makes the most sense here going by the “ages” concept, since mono-Poison Types either represent pollution, are snakes, or are Swalot or Poipole, and we all know later human activity is uh, not great with regards to pollution.
I think it’s why I’ve never been that keen on the new duo, Regieleki in particular. A mono-Electric mon isn’t special at all, we get them all the time lol.