Actually, disregarding the other answer, Ally Switch is technically useable in Double Battles. I know a few people who use it on a Crescellia build, and it works just fine for the format and can actually do some wonders! If it only worked in Triples it would have been cut from SwSh and SV like multiple other moves were lmao.
As for why it doesn't work in Multis? Multi Battles are technically Doubles Format yes, but it's a 2v2. Emphasis on 2. Instead of a double battle, think of it as two single battles meshed together in teams. The other spot is meant for your PARTNER's Pokémon. It wouldn't make much sense if you could just put your own Pokémon in your teammate's spot now, would it? Ignoring that, swapping control of you and your partner's Pokémon sounds like a funny mechanic lol.
Thanks, I hope this information helps! I'm new to answering on this site but I'll be glad to help in the future if any of you can't seem to find the random stranger that somehow had your exact same problem 10 years ago on Quora lmao.