It's a mixture of a lot of congestion issues, including Reigate College (possibly a little less than it used to be, as a few more students actually seem to use the train vice driving in), and other traffic at junctions, but the level crossing causes more than its fair share of problems.
Being extremely familiar with the local area and its trains, knowing many people who struggle to drive around Reigate, and having actually spent some time previously in academic studies developing proposals to alleviate some of the local congestion, it may surprise people that I've yet to be made aware of anyone (myself included) who's been able to draw up anything close to a viable idea to remove the level crossing. The busy nature of the road and railway are compounded by the well-used and valuable offices and housing in very close proximity, and the fact that absolutely none of the local residential roads can accommodate any more traffic without major rebuilding - and not least also the issue that the access to the parallel A242 is also hard to deal with.
Local ecology and landscaping rules mean you couldn't really build much of an additional route to the A242 Croydon Road without going all the way over to Merstham and back, so you can't bypass the A217 from the M25 to Reigate town centre very easily. In fact, if the A217 itself and the level crossing weren't there, it would make for a very pleasant grid of quieter residential streets, stretching parallel to the railway and over to the western outskirts of Reigate.
It's not possible to create a further embankment for the railway without overshadowing the whole of the Holmesdale Road and Reigate College area, so you can't raise that (frustratingly, though, it could probably be done to the west of the crossing). You couldn't keep the value of the local landscape by raising the road, because you'd have a lot of offices and houses overshadowed by an enormous bridge capable of carrying diverted M23 traffic over a two-track railway. You could dig a tunnel from the Castle to the bottom of Reigate Hill, where there is just enough room for it to emerge, but I'm not sure the local cave structures would allow it, and in any case you'd be looking at a fairly narrow set of tunnel entrances and a prohibitive bill, with the need to still maintain a crossing for local traffic in the absence of a road diversion. You could lower the railway, but acceleration from Reigate towards Buckland would be a problem for trains during leaf-fall, not to mention the need to reconfigure the earthworks from Doods Road to the crossing on the east side of the A217. The latter would probably be the most feasible, but at enormous cost, possibly requiring electrification to help with train performance. Oh, and you'd have to eliminate Reigate SB unless it was somehow possible for it to suddenly perch on stilts above the railway.