Throughout history, they’ve gotten into big conventional fights and are renowned for how well they do in them. It is easier to switch from COIN warfare to conventional than vice-versa.
That is an outright lie! Sorry to put it so strongly, but who ever wrote that is talking utter garbage. It is absolutely not true, and entirely false. -what is more the British Army has proved this wrong over 100 years. The British Armies that did COIN from 45-95 where all Hi-intensity, nuclear war focussed forces! - FACT.

A lot of COIN concerns the Restriction of Force. If you don't have the levels of force to restrict, then you are lost.

Good armies can do both. This COIN-v-Conventional is utter BS. This is what is so dangerous about the COIN avant-garde, who seem to want to force the choice.

It takes less training to adapt a conventional force to COIN that it takes to turn a COIN force to conventional.