What are your options? Would she take a year off or try to get into another school if the coach won’t give her a guarantee? She could ask that question herself (“Coach, I’m really worried as coach X said I’d have a spot on the team and now you are saying there will be try outs. I love tennis and being on the team was a major part of my choosing this school”) so I don’t see the point in your getting involved with the coach at all.
In the 4 years my daughter was in school, I only contacted the coach twice, once to get a ticket to an event for my mother (it was a sports fundraiser and it was sold out) and at the end of the first year to discuss D losing one scholarship and hopefully getting a replacement (turns out she didn’t lose the first so all was fine). I don’t see what your getting involved could do at this point. The new coach won’t promise her a spot on the team or to be #1 on singles until she sees her play.