After more thought, I think solo heal would make more sense than solo tank. Why?
Supports would require fewer reworks than tanks: There are four main supports and 3 off supports. Of the off supports, it would be fairly easy to rework Lucio and Brigitte to be main supports. Zenyatta could realistically have his healing toned down slightly and go into DPS. This is much less significant than the major changes needed to tanks to allow solo tanking or making Roadhog, Dva, and Zarya DPS. Zenyatta is already a hybrid.
Synergy is a huge deal to tanks but less important to supports: Synergy and tank-tank interactions are hugely important to the fun of tanking. Support synergy is much less important and isn’t really related to the fun of the problem.
You need two tanks more than two supports: This may just be subjective, but I feel like the team suffers much more by lacking a second tank. Solo tanking also is much more unpleasant than solo healing (again, subjective).
Adding support utility to DPS is easy: it’s very simple to add support healing to DPS heroes. Adding support tanking is much much harder.