For the last decade and a half of my working life I have been priviledged to work in some of the most interesting, beautiful and dangerous places on earth. I carry on me at all times two vaccine passports, one has my Yellow Fever details, the other a set of vaccines specific to hygiene and water for a number of things such as Typhoid. Keeping up and having constant proof of these vaccines is a core requirement of my work. Am I forced to take them, no, there are literally hundreds of jobs I could do that would not require me to have them but I do keep them up because to not do so is incompatible with the job I want to do.
You are right the COVID vaccine mandate may go away tomorrow, but it also may not and if it did go away, the day after tomorrow another vaccine might become mandatory, one that you know as much about and trust as little. The military has had vaccine mandates for decades, a couple of hundred years in fact, COVID might come and go in a year more but the mandates will remain and evolve. Your daughter is not forced to take this or any vaccine now she is an adult, there are literally hundreds of jobs she could do that would not require her to have them, but military service is not one of them.