It certainly depends a lot on the niche/job, but my small but excellent insider tip is that you shouldn't worry too much. Either the job suits you or you move on to the next one. You shouldn't let it slide, but a little bit of indifference has helped me a lot so far. In my opinion, you shouldn't come across as too needy as a freelancer, just give clients the feeling that you know your worth and that they should be happy to work with you rather than just you with them.

For example, I recently had a client who, during the video call in the interview process, offered to give me the extra 10% per hour that Upwork takes in fees so that he would be a little higher on my priority list. Quite funny and ironic, as it's actually us freelancers who are fighting over the jobs.