Hitting Putin on sport is hitting him where it hurts to be fair. I sympathise with the clubs and athletes that have done nothing wrong and I don't agree with stupid bullshit like expelling normal Russian people from other countries or universities or whatever, but I do think the sport thing is quite important.
Putin obviously sees sport as something that gives him some sort of power, or being seen to be the man who brings the benefits of international sporting events to the Russian people. I'm not going to pretend to understand it inside out but if there was no power in sport, you wouldn't see billionaires from seemingly unaffiliated places across the world buying your Chelseas, Man Citys, PSGs, etc.
Putin and his administration sponsored the doping that went on at the Sochi winter Olympics because they got something out of it. Look how great our country is to win all of those medals. It all plays into the Mother Russia angle. Look at that football club owned by a Russian man winning the Premier League and the Champions League. Russia has influence in these great sporting tournaments. Look at our Formula 1 race, Russia can host these elite sporting events just like all the other major countries, I've brought this to our great country and to you. See also the Champions League final which they've had taken away. These events are marks of status, otherwise you wouldn't have Russia, Qatar, UAE, Saudi Arabia, etc. investing obscene amounts of money in bringing as many of them as possible to their shores.
None of this is seismic and isn't going to bring down Putin or peel his oligarchs away from him in isolation, but the best strategy here is to try and put him down with death by a thousand cuts. Putin has consolidated his power internationally and domestically with sports-washing, by allowing his capitalist oligarch class to grow rich with the help of their dealings with the West and the wider outside world, by opening the country up to the benefits of some integration. If enough of these institutions turn their backs on Russia because of him, it does have an impact when you add it all together.