We tried it pretty well back in the 1970s. It was not uncommon to see LP powered conversions on the road. People even experimented with wood gas systems. The problem with LP, at least where I lived, was those engines didn't start well in cold weather. And the second issue was regulations required fueling stations to have someone(s) trained and dedicated to doing those refills. It was deemed not safe to let the common man, (you know morons), do that. That added to the cost. And finally, with an LP tank in your car, you could be driving around with a possible bomb or at least a BLVE under your ass. Which is not safe for those around you.
Sometimes to day you will still see LP powered delivery vans rolling down the road. So it hasn't totally gone away.