Oh, you got point 1 backwards, if you have too low HP you may not hit heal cap.
For point 2: my favourite example (and only one I know) - Atum.
Her heal is 20% max HP, cap of 2k. She needs a target with 10k HP to hit cap. With 2x UE staff 30 slvl she has 30% max HP heal, 3480 cap, 11.6k target's max HP required to hit cap.
Now, I assume that heal acc work similar to Ascension, so with 2x 5% heal (this better kind) and 2x UE staff we get: 40% max HP heal, 3680 cap, 9.2k target's max HP required to hit cap.
In worst case it's 11.6k HP, so not that hard to hit, but let's get her buffed version, which according to JP wiki get her cap raised to 3k, but no change to base heal (still 20% max HP).
With no heal bonuses: 15k max HP required to hit heal cap (3k)
With 2x UE staff: 17.4k max HP required (5220 cap).
With 2x UE staff and 2x 5% accessories: 13.8k max HP required (5520 cap).
It doesn't look terrible in any case, but 17.4k max HP may not be easy to hit (at least not for everyone), so I would say that Atum do likes some nice healing accessories. I would bring Lugh here, but from what I've heard her assist doubles received heal and not only rises cap, so there's no point bringing her here.