The typical lead car battery has a fair bit of capacity. People expect to be able to leave their headlights on, radio on, that type of thing. The LiPo pack would need to similar or greater capacity to meet expectations. Also, there would need to be a LVC, HVC, and some sort of active balancing. The alternator would also need to be modified. Should the battery hit LVC, it would essentially need to simply disconnect, ideally. This would mean nothing inside the car would work. Dome lights, keyless entry, etc. As we move towards vehicles becoming increasingly reliant on having power all the time, this is far from ideal. At least people are 'used' to how the car reacts when the lead battery dies.
It's just not practical. It would take a bit of work to implement safely, and would likely cost many times more than a lead battery for minimal if any real benefit. You see a 5AH LiPo crank a car and think it could simply be dropped in, when that is far from the case. That's pushing that battery to the limits and not quite ready for consumer use. Possibly in a few years it might be more practical, but it will most likely remain the more costly alternative for a long time.