Because by definition, FT/HFT are air rifle disciplines.
Now, one could envisage FT-style events with rimfire but there are a few considerations.
1. Selection of targets and ricochet hazard. Rimfire pings back off hard things (as do air pellets, but rimfire rounds are carrying an order of magnitude more energy).
2. Back stop. No "bird" targets in tree branches (unless you've got a big berm handy). .22lr will do a mile under ideal circumstances so all shots need a solid back stop. Course setting becomes much more complex, and you need a much more substantial risk assessment.
3. Competitor's FAC conditions. Individuals with hunting conditions on their ticket will need an open condition, and/or the land will need clearing. Individuals with Target conditioning (those using CZ452s for NSRA LWSR for instance) would be prohibited from participating because their conditions include wording that limits them to "ranges suitable for that class of firearm with adequate financial arrangements re: liability" (i.e. insurance).
4. Regardless of FAC conditions, you need insurance full stop. To the order of ~£10m third party liability should do it.
If you want to get insurance and have target shooters able to compete, that takes us back to point 2, where the risk assessment is bordering on a range construction plan. Except there's nothing in the manual on building a range like that, so you're going to have to write the book yourself and get the insurers to approve it.
It's not that it couldn't be done, but compared with checking for footpaths, setting some air targets in a wood and posting tape/warning signs, the (paper)work and ground works that would be necessary to safely set up and manage a dispersed rimfire operation would be mind-blowing.
"A fear of weapons is a sign of retarded sexual and emotional maturity." Sigmund Freud
Shooting is my meditation