My husband and I have bought numerous classic cars (both from Craigslist and eBay). And we always paid for inspections done by someone familiar with that manufacturer, era of vehicle, local to the location of the vehicle, etc.These inspectors are almost always referred by someone we know that's used the inspector before.
Would we pay for an inspection if we were to buy a family daily driver? Yes, possibly. But we would use our local repair/maintenance shop to do the inspection - not someone hired by a website owner, like Craigslist.
And I would never accept an inspection paid for by the seller. Too much opportunity for a conflict in interest.