Think about it for a moment, if there were no penalties to dodging then people would be leaving left and right the moment that anything happened that slightly lowered their perceived chances of winning. At the moment there is relatively little drawback, but enough to incentivize people to work something out instead of jumping ship if someone picks a champ that wasn't played in LCS recently.
Of course there are always going to be those who do not want to work with other people, who want a specific champ in a specific lane and woe to any who try to suggest otherwise. But this is a team game and working with others, even those you may not like, is something that you are going to have to do.
If you do not like the idea of your enjoyment in League being dependent on 4 other random people I would have to suggest either playing with friends or playing a game that is not a team based strategy. But remember in the end that your enjoyment and you satisfaction come down to you alone, you can have fun trying out strange different team comps (and honestly a 5 man push strategy is far from uncommon, its won quite a few competitive games) and you can even have fun while losing if you put yourself in the right mind set.
So with that in mind what I would have done is pick a champ that synergizes with a super push strategy but could also help the team keep it up, like Alistar with his team heals and his ability to tower dive. Then you make like Nunu Bot and push the lanes to your hearts content.