I should have chosen my words better.
With a tank you need to heal nearly every single turn, if you use Radiant Light your Tilith is essentially pinned down, and she can't do much else, fine for straight forward battles, but harder ones like Marlboro she's near useless.
Essentially you're losing all utility to keep your tank healed.
If one of your units dies, then she has to revive all, great, but then your tank or other units aren't healed, and they probably need healing if your unit actually died with a tank on the team. Without that heal you could be losing other units, and things can easily get out of control. And that is the most basic and crucial role of a healer.
When you want MP charged, deal with status ailments, or any buff applied, you're stuck. As you said, she can't do multiple things at once, she quite simply isn't a consistent healer if you want any utility out of her. Given that we are now experiencing trails that can last dozens of turns, and sometimes nearly a hundred turns, you can't have a slot filled by a unit that can get pinned down doing one thing.
The reality of Tilith is that you need to supplement her with yet another unit that can help her. For instance a Rikku to support, or a singer, or have Tillith on Prism Heal to keep MP charged, and do actual useful things in between, and have a second healer or support to help her out. Using her for Radiant Light duty is a complete waste of a slot.
Ayaka, by comparison, can not only revive but heal, or deal with status ailments, or dispel, or even re-raise all in the same turn.