r is for running
Some top cross riders claim to do no running at all, while others are convinced that pounding the trails allows them to eke out advantages come race time. But unless it’s an absolute quagmire or you’ve bust your bike, most modern cross involves very little sustained running. Instead it’s required in awkward fits and bursts on surfaces Parkrun wouldn’t touch with a bargepole (there’s a reason you’re not riding your bike at this point).
If you are going to bother slipping into some trainers for the sake of your cross performance, there are two things worth considering: it’ll at least familiarise your muscles with the movement of running; and it’s worth doing some intervals that recreate those tricky race scenarios.