I had an incident with a modern car several years ago with Insurance.
Young girl flying down an icy street rams into my car parked along the curb. Really does a lot of damage.
My insurance company (somebody in Seattle) calls and says they are going to total the car. The next day, same company, I get a call from somebody in Indianapolis says 'we are going to rebuild your car. Where do you want the work done?' and I say OK, tell them where to fix it, they flatbed it there and the car is fixed.
A few days after I get the car home the Seattle office (remember his is MY insurance company) calls and starts bawling me out for having the car repaired. I told them 'That is your problem. You'd better call (gave Seattle the name and number of the Indianapolis office that had called) and YOU can yell at them' and hung up.
Never heard from anyone again
In response to the original post about Liability, before I got Hagerty and had my regular car insurance cover the old cars, I'd call in October and drop all but Comprehensive, and then call again in about April and put it back on full coverage for the driving season. With Hagerty (or Grundy they are good too, or JC Taylor or other old car insurers) you are covered 365 days a year. And the price with Hagerty was less money than what I did before PLUS my everyday insurance did not have 'Agreed Value' you are at their mercy!