I didn’t see a branch of ROTC mentioned here but the scholarship following you to any school is absolutely not true for the Navy. For an NROTC scholarship you apply to up to 5 schools and they award it to a specific school- which you must also be accepted to.
My son is currently a senior applying to 3 acacdemies and 2 ROTC scholarships. He had to apply to 3 members of congress as well. So far he’s written about 12 essays, had seven interviews, 3 different fitness tests, medical and eye exams. Started the process in July. It is intense. He is a 3 year JROTC, commander of the Raiders team, won an AFJROTC scholarship to get his pilots license over the summer. Depending on your district, and all of the work involved, a service academy acceptance in my opinion is less of a “lottery” than the Ivy’s because it seems they truly get to know the candidates through this process and if you can get through all of the application hoops you have a decent shot.
An anecdote about prestige. My daughter’s dream school was Princeton where she wanted to dance in their ballet company and major in math. She checked all the boxes - perfect ACT score, graduated with excellent grades from a boarding school ranked in the top 5 in the country that sends 30% of their senior class to Ivy’s. Classically trained pre-pro ballet dancer was her interesting “spike” among other EC’s. Excellent LOR’s. She did not get in. She did not get in to Amherst or Vassar or Williams (WL) or a few others. Did get in to Hamilton and Colgate. Got a full tuition scholarship to Pitt and Bama. Turned them down for the Hamilton “prestige”. Hated it and didn’t go back after first semester. Fit with a school can be a very real thing. She thought she would be fine anywhere. This year she transferred to a school with a wonderful reputation but not super prestigious and is thriving. Find some safeties that you LOVE.