Can I keep this real simple? The car has a set of conditions under which it much operate. And as others above have indicated, they are pretty significant. The requirements include a solid performance pattern for component quality.
Bottom line... the reason for relays over solid state devices is summed up in a single word.
It's cheaper to provide relays than it is to provide solid state devices to perform that function. When solid state devices come down in price below that of relays, then the automotive manufacturers will switch over to solid state devices. Cost is a major driver when it comes to decisions like this.
A 10 amp relay costs 10 times as much as a 10 amp automotive grade
power mosfet. – Passerby
So, I'm not quite sure that's a fair comparison. I'm thinking most automotive relays carry more current than that. (25 to 60 amps?) Additionally remember we're totally isolated between signal and output with the relay. Assume the Automotive OEM's would want to keep that isolation concept. What the cost of a opti-isolated 30 amp mosfet going to run? Oh, and better place that into a nice plug in container, best if its a perfect drop in replacement for an existing relay.
Additionally there is one more factor related to PRICE. Remember there are suppliers out there somewhere who have invested millions and millions of dollars to automate and tool up their relay manufacturing plants. Additionally they employ a whole bunch of folks. What do you think those guys charge for relays? Answer: As much as they think they can get away with. Guess what happens when the automotive Original Equipment Manufacturers (OEM's) tell those folks they are thinking of switching over to Mosfet technology... you guessed it, there is a immediate drop in price. It may not matter that they are losing money, they've got huge amortization and fixed costs and lots of employees.
It would not surprise me that a true price advantage of Mosfets over relays gets delayed in implementation for purely business reasons for a period of say five years. It would also not surprise me if some of those businesses had sweetheart deals with the OEM's (e.g. I want to invest a lot of money in my process to reduce my labor costs and therefore my price to you, but I'll only do that if I have a five year contractual commitment for product.)