Consumer automobile manufacturers can use shared platforms because the biggest difference between their vehicles is the body, which are metal boxes of different volumes. This is sometimes seen in aircraft: look at how many models of 777 Boeing produced.
Automobile manufacturers couldn't, for example, have a shared platform between a vehicle designed for racing, an armored limousine, and a golf cart, as these vehicles have different performance requirements. That's a better comparison to to what they're trying to achieve with the F35. The needs of the branches of service are very different.
I guess that in the automotive industry different models are often only done to achieve price differentiation or to serve local markets. The technical differences are superficial.
Some platforms just can't be shared. You're not going to be able to turn a Lamborghini into a body-on-frame truck without changing basically everything.
My understanding is that in the aerospace industry, particularly at the cutting edge, margins are so low that common platforms don't really work out.
In the car industry, say, a 10% penalty in, say, weight might be worth it if it enables the manufacturer to share the platform among many different products. In aerospace, not so much.
I think the VTOL in particular was too much of a stretch. If you see the complicated drive bar setup with that big fan, it really makes me wonder how this thing could possibly get airborne :)
Also, maneuverability and short wings go together really well. Slow flying and short wings doesn't though.
Still, it was clearly a mistake, three totally different designs would have been cheaper and better.