Just my opinion, freelancers that race to be the first few applications in will not bother to change the budget. When we apply for a post the budget the client states is automatically filled in and we have to change it. The bot proposals and copy and paste people who are trying to be the first to get their application in is probably not going to bother to even change the budget.
I know this because I have one client who will way over budget his projects on purpose. It's one of his strategies to hiring and determining if a freelancer is honest, and he says 70 to 80 percent of proposals he receives are for the budget he stated.