Or, it's that playing a support is complete ass in anything but raids. It's the complaint I have heard the most. It wore me out after over a year of playing two supports.
Your understanding of support gameplay for daily content is based on dated information. It would be a correct statement if we were talking about the Brel era. Anyone who knows what they're doing these days would not use Betrayal for instance when clearing Chaos Dungeons, which would have been a status quo for you at the time. You can very easily make a support build to clear Chaos Dungeons in <3 minutes per clear.
Towers would still be annoying but I haven't done a Tower in over a year. It's not relevant content. The potential +30 seconds you take on this stuff is reduced greatly for all of the perks that one gets for playing a support, specifically;
1) Any support is able to get invited to a current Guardian raid lobby and get in with a juice grouped that will clear 1-2 minutes quicker than matchmaking.
2) Any support is able to get invited to most lobby's without wait time and their character requirements are laughably low (the express pass gems give you gems that are better than what anyone will care about). I would not accept a DPS with lvl 7 & 8s gems however I would take a support with these easily.
The issue is the same as any MMO. People don't like playing the support bitch. Everyone wants to run DPS even if, objectively speaking, they're terrible at DPS. The big numbers just feel good. There is very easy evidence to suggest that releasing a new support class would solve the issue: when Artist was released, we spent 3 months with an overabundance of supports. Releasing Female Paladin as a support would have the same effect, only amplified by quite a bit as Paladin is already inherently easy to play and would share a similar character model to Slayer, which obviously appeals significantly to most MMO players.