I'd stick with just using a normal relay. Much cheaper, simpler and works well. There's a reason why relays are so commonly used in automotive - because they work.
Although the automotive market is starting to switch to things like MOSFETs for power control, they haven't replaced relays. Usually MOSFET's are used in places where there is a need to regulate current or control a load (like PWM for lights/motors). Or more recently things like SmartFET's or ProFETs which give current and load feedback.
A main ignition switch terminal often handles a significant amount of current and I think you'll find a MOSFET or other solution is going to be far more expensive than a simple, old relay.