Part of the problem is that they maybe work too well. A lot of particle theory is model fitting without probiding us new insights into a possible underlying reality. Or something that would force a paradigm shift. Real evidence of something completely contradictive to our existing theories would be a dream come true.
Modern physics is anything but intuitive in my opinion. Maybe reality isn't well described by real numbers, or maybe it is; but my sense is the reason why physicists have used real numbers is because they've worked pretty well up until a certain relatively recent point, when other intuitions about reality have started to fall apart as well.