The proposed solution (from the OP) would actively harm the game. It would help nothing and increase lag and server stress. The problem is not the number of people trying to complete low level dungeons (though there are few at any given time). The problem is the distribution. The only way this could be changed is for the distribution of available jobs to more closely match the distribution for a 4 man dungeon (1:1:2). That's almost certainly not going to happen and would only be completely effective if you assumed equal distribution of classes played.

To lower the queue times sufficiently there would need to be a significant reward for tanks (and healers) to run low level dungeons. This reward would probably have to be unavailable to DPS, however that might not be necessary since you'd mostly be drawing the level 50 crowd where many more people are playing tanks and healers for a variety of reasons -- sometimes just for low que times.

To say that "it's time to address this issue" is also very silly since it's been a bane to anyone working on their relic weapon the extent to which SE has been (perhaps ineffectively) addressing this issue.