Otherwise you are slowing down everywhere and can only run as fast as other trains on the line, unless you also impact their services by having them pull off.
They are however actively removing crossings and generally everything HSR is electrified.
Even then while it is possible it doesn't work well, as HSR will catch up to whatever else is on the track and then must slow down.. the cost to build HSR track is so high (even at world leading low prices) that you have to run several trains per hour on those tracks to pay for it, and so there isn't free space for lower speed trains in between.
Nobody makes a switch that can be crossed at high speeds so the slower train cannot just get out of the way no matter how much you might wish for that to wosk.