Ditto to what some other posters have said, the average 100% cotton tshirt is not going to give you much protection from the sun, and they do get waterlogged very easily. As a former lifeguard, I've pulled many a little one out of the pool who was wearing a t shirt that was waterlogged, and 3 sizes too big,so it was impeding their ability to swim.
DS has been wearing 'rash guard' or 'swim shirts' for the past 2 years. They ones he has are very lightweight, and are equivilent to wearing SPF 30. They are strechy and form fitting, so when he's playing, he barely knows he's got them on.
Back to the OP--I don't think it's against the rules to wear tshirts, but there are definitely better options out there.