My impression is that the most stolen cars usually fit that description, surprisingly enough. Old, reliable, nondescript cars are exactly the ones that have a thriving market for parts and are relatively easy to steal. I remember for instance, late 90s Honda Accords being on the list of top most stolen models at one time.
The other reason I see not to keep an old car forever is that I don't trust old airbags, especially since the Takata fiasco. Nothing lasts forever, and originally I read that airbags were supposed to last 10 years, so how do you trust a 15 year old explosive device aimed at your face?