Ah, so you're finding them on freelancing websites? I missed where you mentioned that. Of course, you'll have poor writers there trying their luck and hoping you'll accept whatever crap they come up with.Do you really expect the $hit writers will also NOT apply Just because you are offering $100/1k?
Heck.. there will be even more of them to try their luck
It's not the budget, It barely even matters once you go past a certain level.
I hire usually based on recommendations in Facebook groups. High-quality US or UK writers who research and can follow a brief generally charge accordingly though, because they know their worth. So yes, I'd say budget matters.
As you say though, maybe it doesn't so much if you're looking for writers to apply for your job.