Short answer: it's complicated.
Full context answer: Pokemon Colosseum was released at an otherwise never replicated time in the Pokemon franchise's lifespan. Pokemon Red and Blue (and Green and Yellow) were 100% compatible with Pokemon Silver and Gold (and Crystal), so you could transfer your 'mons forward, and use Mewtwo or your favorite Hypno in your "new" Pokemon Silver at will. Pokemon Ruby and Sapphire wisely dropped the backwards compatibility, as the stat balance of Pokemon Red and Blue was not viable going forward, and being able to transfer that 999 Special Mewtwo would just mean the winners of the competitive scene would only ever be whoever had the oldest, most busted pokemon. But, while this was good for the "meta" game, it was terrible for those of us that lived and breathed catchin' 'em all. There were a great many pokemon that were completely absent from Pokemon Ruby & Sapphire, and any previous "legendaries" were 100% out of the picture. You were equally screwed if your favorite was Hypno or Mewtwo.
Enter Pokemon Colosseum. Pokemon Colosseum was touted not only as "better" than the Stadium games by being the first console RPG Pokemon experience, advertising materials also made it clear that this was going to be the only way to (re)capture a number of Pokemon Silver/Gold pokemon. You've got the big three starters, mareep, sudowoodo, the three legendary cats, tyranitar, and Lugia (right there on the cover!). Ho-Oh was a "secret" reward for conquering the battle tower. Whether it was ever outright stated by the Pokemon company, the implication was real: if you ever want to see your favorite 'mons again, you'll do what we say. As a result, some of the most desirable pokemon here (like Tyranitar and Lugia) have atrocious purification requirements, because the game was more or less designed around you doing everything on the way to "earning" the ability to bring those guys over to your "real" GBA games. You cannot transfer a shadow Tyranitar to your Pokemon Ruby game, but you can after you have been a good little player and made that godzilla a real boy (well, girl. You wanted a girl. You couldn't breed 'em without a girl or a ditto, and we wouldn't see ditto again until the Fire Red/Leaf Green releases).
Since that third generation, every pokemon has been able to be "carried forward", so, even if you might have to wait a bit, there wasn't that same drive for "we might never see a tyranitar again". Even now, you cannot yet connect your ancient pokemon in Pokemon Home with Violet/Scarlet, but we are told that feature is coming soon, so the lure of a hisuian zoroark with a DLC preorder is not as "urgent" as it once was to catch and purify a shadow shuckle.
So anywho, love it or hate it, the shadow system goes part and parcel with where the Pokemon franchise was at at the time, and the concept that you would really have to work for your completed 'dex.
It's the Dark Souls of catching a Delibird.