There is way too much deviation from truth in many comments here, including the OP.
1. Money talks. A child whose parents can pay well, even donate to the yeshiva, is more likely to be accepted, regardless of many other factors. Pretty much everyone I know has witnessed this up front, and pretty much every mosod I know practices this way. Yes, we understand that managing the finances of a yeshiva is a difficult task, and funds are direly needed. But we should wonder about the morality of making admission decisions based on the Almighty Dollar when the supposed criteria are spiritual in nature.
2. Mosdos no longer are receptive to input from rabbonim concerning admissions. There is ample case law to share on this. Enough has been published in our media, so there is no reason to give examples.
3. Parents might not always be judging correctly regarding their preferences for where to send their children to yeshiva. But I propose that yeshiva menahalim aren’t either. Resolving these differences isn’t easy, and it always ends up being done by the yeshiva overpowering the parents. Yes, it’s a power thing. And I have a struggle in accepting that this is how the Torah wants it.
4. The notion of “no child left behind” is truly praiseworthy. In smaller communities, this might actually occur. But in the highly populated areas of New York and several locations in the region, this is fantasy. The mosdos are not serving the community, and they do not feel any obligation to aaccept a talmid when there are many other mosdos listed in the yellow pages. The typical attitude of a yeshiva under pressure to accept a talmid is, “Why me?” The reaction should be “I’ll try to succeed with this.”
5. It is true that not every kid fits into every yeshiva. This requires attention by the parents, and once approached, yeshiva administrators need to be the baalei chesed they wish to model for their talmidim, and assist the parents in directing a more appropriate referral.