I see where you are coming from, except for that little "Not like supports aren't strong enough". Squishy support supports like Sona and Soraka are damn strong yeah, so are ones like Janna and Nami. But that's mostly because they've got a heal or extremely good CC, and they can afford to build full AP because of how gold gen works in ARAM. Supports like Tahm, Taric, you know, mostly Tank Supports don't really have heals. Even Taric's is not going to save a team quite like a Soraka or a Sona. I completely recommend any support get Redemp in ARAM, purely because that can save a team. It can win a game. And that's not quite as broken as seeing a Ziggs and Tristana on the enemy team in an ARAM, or one of the other POWER COMPs that dominate.
Also, it doesn't really ruin the mode. Sure, it'll heal a team up a good bit, as well as deal some damage, but it's not restoring everyone's mana, it's not giving people items. The fact that you can't recall isn't just so you can't heal, it's so that you can't coward out after a fight and heal all the way back to full, grab those power spike items, and wreck havoc with your full mana pool. It forces you to choose, "Do I try and survive as long as I can and buy 3 items at once, or do I execute myself now so I can keep up with everyone else who's gotten items," and it forces the enemy team to decide if it's worth killing the 30/0/13 Draven and letting him get all the items.