I don't see the problem - I'm definitely in the minority. I have 3 kids and no family or partner/second parent to watch the kids.
It's it's a village hall type thing, I'll take the one child and then wait to the side or outside with the others but I have to say in my oldest's class they've almost always been welcome. I never let them eat the food or take a party bag
It's it's a soft play place, I'll pay myself for the extra kids and will keep them playing while the birthday party is having food and cake so they don't intrude
If it's somewhere I can't take them (one party was at a trampoline park and they weren't allowed in) then I asked another parent in the class if they'd be willing to take my oldest in and I'd wait in the car
My youngest twins have only been invited to one party so far, but my oldest (7) happily sat with the parents playing on his iPad while his brothers partied
Maybe it's different for me because my oldest was going to parties when the youngest two were literally newborns. I remember taking the twins along to a massive sports hall-bouncy castle party when they were 6 weeks old and not even awake and overhearing another mother (not the party host) tell someone how rude it was that I brought siblings. They couldn't eat, or play, were literally sleeping in their pram or being cuddled by mums and weren't part of the headcount
If it's unclear whether I can "get away with it" I'll always ask. But knowing how hard it is I always make a point of saying on my son's party invites that siblings are welcome.
Honestly, give parents some grace if it's a case of their child misses out entirely. If it doesn't affect the headcount or your cost how is it a problem?