The BBC is a public broadcaster, funded and owned by mandatory license fees in the UK.Clarkson was on contract to the BBC. Once the organization confirmed that unprovoked verbal and physical abuse had occurred, they had to take action or leave the corporation open to an indefensible lawsuit from the victim. They can't exactly say, "Yeah, get stuffed. We have extensive policies promoting equality and prohibiting harassment and violence in the workplace, but we're ignoring them because the presenter is popular and profitable."
No doubt Clarkson and pals will make a profitable jump to Netflix or Sky to make a similar motoring comedy show. Meanwhile, the BBC has a chance to reinvent Top Gear with younger presenters and a reinvigorated format (there are only so many new Lamborghinis, Ferraris and Aston Martins that can be driven around a track in a cloud of smoke every week and only so many routes for contrived road trips through war zones in ancient sports cars).