@ Mrs. Oreo
The reason they limit it just one Pokémon on the field before being captured is because it'd turn into a buffet line if you could go for the opponents' allies. The problem with the SOS battles is the oversight with the mechanics. For example, a synchronizer won't get the nature you want when a Pokémon is called. Opponents can faint each other inadvertently and sometimes intentionally, sometimes they knock themselves out (see Geodude and Beldum). Status happens, it just does and when it happens to an opponent it ends the chain. Other species end the chain. Sometimes there just aren't practical match ups or the opponent uses it's PP up too soon and Struggles to death. And sometimes just about all of these factors happen in one turn!!!
Last Gen, you got to see a Pokémon with an HA, item, level, and decent stats before you even had to engage it in battle! This was obviously incredible. But with SOS, it's just too tedious for something we had way better beforehand. To get the Pokémon with 4 guaranteed stats you need to have fainted 40 members which is a huge investment and stuff can go sideways. To get hidden natures, you have to have a way to trigger them to confirm in battle , not always possible, and f*ck shinies-this isn't 2001! We got the fillet mignon, but now we're stuck with the fatty ground beef.
Wouldn't call it an oversight, more a matter that they probably wanted those special things you want on a Pokemon to be actually difficult to get and require some effort and time.
Everything can be gotten around anyways:
Synchronize-Haven't really bothered with it myself, but breeding can get around this, find a partner Pokemon with the nature you want and just give it an Everstone.
Wild Pokemon knocking themselves or allies out-I believe only Sableye and Mareanie will knock out their ally, you'd probably want to knock those two out first anyways so they can continue to be called out. Not sure on any Pokemon with moves that hit multiple targets, but same deal anyways. Geodude is probably the worst case since it has Selfdestruct but Damp can get around that, Beldum is probably better off not using False Swipe on for Take Down issues.
Status-Don't think anything can place a status on themselves so unless an ally Pokemon somehow does it(Which would be unlikely), it would be on you if you placed the status. Easy gotten around by avoiding using anything that cause such things.
Other species-Just knock out the other species and it's all fine.
PP-Is only an issue if nothing gets called, which could happen, but for the most part you'll likely be able to get an ally Pokemon and knock out the other Pokemon to have a fresh Pokemon.
You need to knock out 30 for 4 perfect IVs. And there is a chance for Hidden Abilities once you knock out 10 Pokemon and chances increases to 15% at 30 knockouts. You'd probably end up breeding afterward anyways, so it's not like you need the perfect Pokemon from SOS Battles, spend some time and effort, get a nice one, and start breeding to perfect it.