Advice?

Hi everyone! I need some advice. I have some trees in my yard that may have some termite damage. Termite guys say they see evidence, which I totally believe they have already killed a rose of Sharon tree that was in the front yard. They also apparently got to the house but haven’t caused any significant damage yet thankfully. I’m getting termite stuff taken care of this week. I had a tree guy come assess and he was very unimpressed with what he saw and seemed to think they were not in immediate damage and don’t need to come down. One is definitely leaning over my carport, so that one they are going to limb up, but leave the rest. What I’m afraid of is them being more damaged than he thinks and of them falling. The one near the carport would definitely fall on the cars if it falls but I don’t think it would end up hitting the house, but of course there’s no good way to know for sure. There is one other that if it fell and was pushed towards the house, could definitely do some damage. My question is if they end up falling on the house and have questionable termite damage, would my home insurance still cover it? They have covered damage from two other tree falls but they did damage property and that was before termites. I have USAA and they were great with the other trees, but again just worried they wouldn’t cover anything if it came down to worst case scenario and they damage the house. Has anyone had a similar experience that can speak to this?