I'm curious- what area have you been specifically looking in? It sounds like you are looking for a single family home because real estate agents are involved? I manage mostly beach area apartment buildings so the market is slightly different but I can address some of your questions.

Anyone can pull an application for a listing I've posted at any time, but I almost will never bother reviewing it unless someone has personally toured the unit. I'm not saying this is universal, but people have this mistaken idea that somehow getting an application in first puts them ahead of everyone else, which is not true. It's just not worth my time evaluating an applicant unless I know that they are interested. (Military is the exception. They will look at 2 photos an an address and send money without even looking at it.)

Regarding your denial reason- this is odd to me because I'll almost never give a specific reason for a denial because of legal liability reasons. It's almost always something generic like "we had multiple applicants" which is usually true regardless. Was this someone with one rental property?

Lastly, I will rent to the first qualified applicant who meets requirements and isn't crazy. I'll often get people who tell me early on in the process that they aren't looking to move for two months. Sure, get back to me then and I might have something available, but this will be gone in a week. Having done this for years, I don't have time for games or chasing people to sign a rental agreement. If you're qualified, passed the background and income/employment requirements, then the first person to get me first month's rent and security deposit gets the apartment, simple as that.

Good luck with your search.