Actually the natural mobility isn't a huge deal. People can fix this with their builds. I know a person who plays Leona and has very good mobility through runes and items. Also consider that while mobiliy is important. It isn't everything, but I'll touch on that in a moment.
Tanky characters do have an advantage to a degree, but they aren't everything. The reason these characters tend to shine is because of the lack of coordination you see in dominion. What you have in dominion is a lot of solo question people. Naturally on a smaller map, if I have enough HP for us to get in a fight and our teams see this and show up, I will live long enough for them to show up whether it be to help or to kill steal.
However if you are like me and tend to que up with friends you will see that other classes shine quite well when you can actually coordinate your movements.
Now back to mobility. Yes its a big factor in the beginning but you only need one or two high mobility chars to win. Good examples are rammus (of course), shaco, garren and trundle. These guys are good to back cap, bottom gank and all around support. But without teamwork and coordination the advantage they bring to the table is useless because if everyone is running around your points aren't being protected. Remember you only need three points to win.