When there are long pursuits the CHP usually takes over if the offender moves some distance away from the original location that the driver did not comply. Also, it is standard in most pursuits for the chasing vehicle, the one immediately behind the pursued vehicle, to not talk on the radio, the second car in the pursuit does that. A lot of times, the officer calling the pursuit in the second car will be replaced with another vehicle that has had the time to make frequency changes. This is one reason you see cars at the front rotate out of the pursuit or further back in line. This also helps with stress control, not being in the hot seat for too long.
The cross band repeat is an important function. The CHP can bring up federal frequencies used on a wildland fire, for example. It is seamless to. They don't need to know that their handheld is on 700 MHz and the Bureau of Land Management is on VHF High. The radio has a display that shows them the channel they are on, say BLM Central California Fire Net, and the radio user just rotates a dial. That is my understanding after looking at a CHP officer's handheld at the county fair in fall of 2019, albeit, very briefly. The officer explained the rest of it to me. He complained to me that CHP radios are crap though and I'm not sure why he would say that. He is too young to remember the 1950's era portables I used in the USFS in the early 1970's. A 40 lb. metal box with batteries bigger than what goes in a car now.