In the USA, the BLM administers some 18000 permits to farmers and ranchers who pay them grazing fees.[0] Then cattle wander on that range exactly as you propose.
The BLM also employs snipers and gunmen to intimidate ranchers who don't pay the grazing fees. Some ranchers respond with impromptu militias.
Sometimes things escalate to the point that goverment agents kill protesters. Sometimes law enforcement officers get assassinated.
But mostly, cattle graze as you suggest and the BLM collects grazing fees.
The BLM also employs snipers and gunmen to intimidate ranchers who don't pay the grazing fees. Some ranchers respond with impromptu militias.
Sometimes things escalate to the point that goverment agents kill protesters. Sometimes law enforcement officers get assassinated.
But mostly, cattle graze as you suggest and the BLM collects grazing fees.
[0] https://www.blm.gov/programs/natural-resources/rangelands-an...