Lots of good points above.
I think what I'd like is to ditch all the national and international controlling bodies eg UK Athletics, FIFA, IOC, IAAF that are really self-serving and ultimately corrupt when big money is in play. The whole idea of national teams. Bernie Ecclestone too. Even the concept of local football clubs/teams seems rather silly nowadays given that most of the players and supporters are spread worldwide.
Would prefer something more cause/charity based - eg like the London Marathon, where organisations can put forward competitors to raise money for their causes. This could still all be supported by sponsorship (ie advertising) and media also lotteries etc, but we could do without building of grand stadiums, villages, roads and so on ... that are useless after the event.
It is true that I haven't thought through how it would all work..
I don't have any problem with teams in team sports.
And once you need a team, such as in football, I also have no problem with having some competitions where they are club based, and not unreasonably based in towns and cities. It doesn't matter to me whether the players aren't local - it is the club that is historically based in a location, not the players who necessarily come and go.
Nor do I have a problem if some team game tournaments are based on countries with eligibility criteria. In fact I rather like the different approach this gives - that you cheer someone to the rafters when in their club shirt but not in the country shift and vice vera - all good fun and a natural extension for a team sport.
But I've always had a problem with trying to pretend that individual sports are team sports - more so that they are somehow country based teams. So Usain Bolt isn't really running for Jamaica - he is running to win as an individual, and he will do absolutely everything he can to beat some of his sternest rivals - who just happen also the be part of the same Jamaican 'team'. And they will be doing the same to beat him. It is an individual sport so no 'team' is required - just the individual competing against other individuals.