How do you know they are "sure able to fund their team to travel the country and play on ESPN"? I'm an alumnus and am next to certain they don't have anything like the funds needed to fly to several games a year. Also, it's not what the school is all about. To play a "national schedule" you have to make arrangements (especially academic arrangements) that would not be compatible with what the school is all about. They play one game a year that requires them to fly to the location, and so far it's always been a game played before classes start. You mention St. Peter's. They've played them several times. They've played the Jersey Bosco team several times. They've played IMG once and will play them again next year. They've also played St. Frances and St. John's (DC). This year Buford (GA) was to come to Philly but backed out. So it's not that they shy away from competing against schools with very strong programs.
The Prep has been part of a league (the PCL) for 100 years--or more. There have been some very good teams in that league in the last 15 years: LaSalle and Wood especially, but Judge and Roman have also had some good teams. Do you think the school should abandon the league? Also, many of the schools you mention (St. John's, Mater Dei, St. Thomas Aquinas, Bosco, etc.) are also part of leagues. That means they have league game commitments most of the season.
You ask what the difference is between SJP and the schools you name. I can't say I know a lot about all of those schools--do you?--but I'm pretty sure that the Prep is more academically demanding than at least some of them. A look at the schools' websites suggests there are other differences as well. Start with facilities.