Purely focusing on the political issues and ignoring ethical problems they cause inside the host countries:
Olympics have always, and will always, be a political tool. They are a great way for a country to celebrate themselves, change (inter-)national perception, and are generally one of the very best ways to sportwash ones image.
For the best documented case there are a ton of great articles/books on the 1936 olympics in germany. If youre remotely interested in sportwashing then thats one of the best places to start.
Its generally held relatively black and white ('tis the way history goes after losing a war) which makes it a lot easier to grasp the critiques using concrete examples compared more nuanced modern articles.
There are also detailed write-ups that I know of for China and Russia (and im sure for a toooooon of western countries too, who ofc will also be abusing the olympics for their own gain).
Heck even this years are already surrounded in political controversy with the snap election.
Then theres boycotts galore for political reasons. People accusing their political enemies of cheating etc.
Its a mess, deeply intertwined with political bs, that misuses sports. And now esports.
If you want a lighter critique try and see if you can find an online version of "Asterix at the Olympics Games", that ones at least fun to read, even if its messages are a bit more veiled.