I have a bit of experience with being a high level white mage and summoner myself
And I'm in the 60s with black mage and red mage... so I've seen a few things.My belief is that red mages should be willing to take more of a healing role in a party that doesn't have a white mage in it, especially as you get closer to 75.
The problem is, if you have a summoner in your party, they can only cast up to cure 3, and they don't have fast cast.
So, if your tank gets seriously hurt, the best the summoner can do is use cure 3 (maybe if the ten minute timer isn't still ticking, they could precede it with Divine Seal). After that cure 3, which might heal about 200hp with a light staff, the summoner either has wait for the recast timer to cool down to use cure 3 again or they could cast cure 2 immediately instead.
As a red mage, not only do you have cure 3, but also cure 4, and you have fast cast. And when a monster is chewing a ninja's limbs off, every moment counts.
Also, once summoners get into their 70s, they have damage dealing attacks that are pretty decent. I think it's probably more efficient, xp-wise, to let the summoner damage deal and backup heal, as needed, and let the red mage deal with curing the tank for the most part.
All that said, there is one situation where a summoner shines at healing above a red mage and that's when several party members are hurt at once while the monster is still alive. Using Leviathan's Spring Water or Carby's Healing Ruby 2 will cure all members of the party quite nicely (at least the ones in range), but the summoner won't get any hate from it. Contrast this with what happens with Curaga spells and you'll see what I mean.