I think a good solution to getting people to play support is by revamping the Secondary role
Queue times are high, and Riot wants to lower them. One of the main causes of high queue times is the lack of Support players. I think that a good way to get people to start playing Support more often is by making an exception for those who put it as Secondary and allow them their Primary roles more often.
Putting Support as your secondary role pretty much guarantees you Support regardless of what you put as Primary. I doubt anyone has it as Secondary because of it, relatively making Support Mains the only people who play Support. If the system allows people their Primary role more often, people would be more willing to take it as Secondary. This would increase the number of support players and also lower queue times.
Hell, I'm a support main because I dislike having to play 2 roles out of Top, Mid, Jg, and Bot, and Bot/Supp just meant Support.