At one time, Burger King ran an ad that there were a thousand ways to have your Whopper. (ten condiments that you could have or leave off, I think.) If you're not going to back that up by actually doing it instead of just making assembly line burgers, don't advertise that.
And McD's, which is what Sparky McNosalt up there was talking about, has never advertised that. BK's pretty much always stressed the "have it your way" thing, because when they and The Clown were the only games in town, that's what set them apart.
So, yeah, if I go to BK and I want no onions, I order it without onions. If I go to McD's and I want no onions, I suck it up and scrape them off.
You know, it's not like McDonald's is inflexible. Hell, it's not like ANY fast food place is inflexible.
In fact, I find that Burger King seems to get it wrong the most often, and not just my local one. Literally every Burger King I've been to has no idea what "no tomato" means.
I still don't see how it's "annoying" to make one custom order. Everything's made to order now anyways, so does it really matter if they have to make ONE batch of fries without salt? Or ONE burger without pickles or onions?