Doesn't have to be BA. It is not correct that all OW airlines require 4 paid flights on their metal. This might be the rule, but not everyone is enforcing them.

Plus, this is only relevant for status anyway. If you wouldn't get status this problem doesn't exists for you.

So the main question is: What would you like to get from your program? Lounge access? Award flights? Lifetime status?

If award flights is what you want, then have a look at AA. They have a good earn/burn ratio and low fuel surcharges. There are a few traps with them as well but the detail depends on your flying pattern and the booking classes because a lot of discounted economy only gets 25% and then AsiaMiles is more attractive.