Cauterize is the most popular and most effective item in the most situations. It's a good pick even against a team without supporter! Just because it counters the selfheals realy effectively too.
The high basic ally heals makes the item Veteran pointless for the team mates, because the healer will be heal you to full hp before your self regeneration starts so often.
The other part of the problem is that e.g. damage dealers cant increase their damage with cards, because it would be OP, everybody would use it. But supporters can increase their heals with cards, so these cards are literally always used in their loadouts. If these obligatory cards would be removed from their kit, supporters wouldn't have just an obligatory pick in their loadout, so these would be much more unique, what is the aim. I think these heal cd reducer cards makes the heals too much, these are too important picks, so makes the loadouts easy to make (use this card on high level) so the game would be better if these cards were removed.
I don't want to make the supporters less important and I already explained why Cauterize is OP even not against healers so if both sides were weakened than the total heals wouldn't changed so hard, but Cauterize wouldn't be just an obligatory pick and supporters loadouts would be better, because there neighter would be an obligatory pick.
If the certain supporter has no direct heal cd reduce than I suggest to nerf the card what helps him/her to heal in any ways. If the supporters heal depends on a card too hard than I suggest to reduce its heal base cd by a little for keep the supporter useful.
Reduce Cauterize' bonus from 30%/lvl to 20%/lvl and make the heal system similar to the reload system: 60% would be the new the limit, sinstead of the current 95%.
Replace the cards of the supporters:
Furia:
-Light Forge: Healing an ally garants {12|12}% damage reducetion for 1s.
-Reduce Solar Blessing's heal from 300 to 60.
Ghrok:
-Gale: Enemies has {16|8}% slow in the area of the Healing Totem.
-Reduce the cd of the Healing totem from 15s to 12s.
Grover:
-Perennial: Blossom garants {80|80} shield up the 2000.
-Verdant Expanse: Its area increasing is only increases the area of his passive heal.
-Adrenaline: Reduce its scaling from {10|10}% to {8|8}%.
Jenos:
-Retrograde: Astral mark decreases the lowest active cd of the ally by {0.3|0.3}s.
-Astral Cycle: Astral mark decreases the highest active cd of the ally by {0.4|0.4}s.
Mal'Damba:
-Eerie Presence: Reduce its bonus from {0.5|0.5}s to {0.3|0.3}s.
Pip:
-Reload: Heal an ally with Healing Potion garants {8|8}% increased reload speed for 2s.
Seris:
-Soul Forge: The healing channel deals {20|10} damage per 0.1s to the enemies who are touching it.
-Reduce the cd of Restore Soul from 4s to 3s.
Ying:
-Spring Bloom: Reduce its bonus from {0.5|0.5}s to {0.3|0.3}s.
-Carry On: Reduce its bonus from {1|1}s to {0.6|0.6}s.
-Reduce Life Exchange's heal from 800 to 500, but it heals Ying (by 500) if it used on an enemy.
Io:
-Protectors: reduce its bonus from {2|2}% to {2|1}%.
Torvald also acts like a supporter, but heal main help is shielding. This is why his shield cd reducer card is OP. So Timeshaper should be removed. I would replace it by the following card:
-Savior: Protection grants {6|6}% increased healing to its target for 2s or until the shield exists.