I don't see the benefit of buying it before final payment. I have not noticed prices changing if you wait, and companies will sell you a policy up to the time you travel. I have a 2 week trip to Belize coming up next week and just bought insurance last week.
If you travel frequently, especially involving travel out of the country, purchasing an annual policy may be the way to go. I looked into it for 2023, as we already have 2 trips abroad planned early in the year, but I didn't pull the trigger. I definitely think when my husband and I retire (within a year or so), we'll just get annual policies. We are currently primarily only interested in coverage for medical, evacuation, trip delay costs, recovering delayed/lost luggage costs.