There is CFI "hull" insurance. However, like renter's insurance, it
only pays when the CFI is at fault.

https://www.aopaia.com/cfi_insurance3.cfm

Optional Coverage - Limit of Liability (Physical Damage to non-owned
aircraft):
Per Occurrence Annual Premium
No Coverage 0
5,000 125
10,000 175
20,000 250
40,000 450
60,000 600
80,000 775
100,000 975
150,000 1,425