Mainly insurance but also aircraft complexity. If you went for a midsize cabin biz jet, guys/gals with lots more experience would also be applying and frankly be much more employable than you.
My advice, keep flying your twins to get more experience. If you really can't wait for a piece of the action do what has been suggested, go for a CJ/C525, Phenom or Premier (of the three CJ is best option).
I know of at least 2 UK operators who won't touch you unless you come with a CJ rating!