how to fix new champ select and incentivize filling
TL;DR If someone fills for a game, let them play their primary role guaranteed for the next 2-3 games.
The current problems are well known. Many people don't like to play support. Many people including myself are willing to take a turn playing support but do not want to play support regularly. The new champ select absolutely sucks in this regard because if you select fill or support for your secondary you will wind up playing support most of the time. Therefore we end up doing things like picking the most highly demanded role (mid) as our secondary when we're sick of playing support, and then to rub salt in the wound we still don't get our primary role and end up playing mid when we don't even want it!
The current attempt at mitigation is to make match making search harder for primary roles before falling back to secondary, but this does not solve the fundamental problem with the way the current champ select works. First of all it still results in playing support multiple games in a row, so we are STILL forced to pick a third role which will also take playing time away from our primary role. Second, the mediocre increase in likelihood of getting your primary role over your secondary comes at the expense of increased queue times for everyone.
Typical scenario when I've tried to give the system an honest try: Game 1: Queue Bot/Fill, Play Supp Game 2: Queue Bot/Fill, Play Supp Game 3: Screw this I don't want to play three Supp games in a row, Queue Bot/Mid, Play Mid (Rito Pls!!!!) Subsequent games: F*** this s*** I'm queuing Bot/Top and playing Quinn every time I get top.
The way to fix this problem is to let me take my turn being a team player and filling for a game and then reward me by letting me have my main role for a few games. Since the four roles other than support aren't equally popular, it's not quite as simple as saying, "If everyone just played support every fifth game, we could all play our main roles four out of five games." I don't know the exact numbers or math involved, but I would think the difference in popularity between bot and mid is small enough that filling every fourth game could enable people to play their main 3/4 of the time if how often I get mid when queuing bot/mid is any indication. If not, then at absolute worst I can't imagine filling every third game wouldn't be enough to ensure being able to play your main role 2/3 of the time. Or we could even adjust the numbers based on the popularity of each role (e.g. mid and top mains use 2/3 and adc and jg mains use 3/4). Or if you want to maximize the system (at the expense of making it more complex for players to understand) maybe calculate more precise fractions rather than awarding an exact whole number of games per game filled.
Considering how unpopular support is and how much problem it causes for queue times and matchmaking, it's really silly that there aren't any incentives at all for playing support right now. Faster queue time is not an incentive when you're stuck playing something you don't enjoy when you get in game. ("Oh goodie, I get to hurry up and start supporting sooner!") I don't know why Riot has ruled out IP incentive, but whatever. I get that some players don't have a use for IP, but it would sure be a nice incentive for those that do. I would feel a lot better about playing support if I felt like I was getting something out of it other than being a martyr.
I'll close with one more idea. How about experimenting with a 4v4 game mode? Three solo lanes and jungler. No one has to support. It couldn't hurt to try it.