You might have already been told this.. I don't know, but I'll tell you anyways,

BHPL (break hp limit) is an over-rated ability

With BHPL if your character dies and is auto revived, that character will have ~10k hp which results in you using precious turns healing to full hp and auto-potion wont heal over 9,999 hp.

Celestial weapons attain their full power when a character has full hp
Lets say Tidus was killed (99,999hp) revived by auto-phoenix he now has 9,999hp even with an x-potion (less recovery time then manually using Curaga) he will still be below 50% hp and his weapon will be weakened, you would have to waste a turn of dealing 99,999dmg, and instead heal Tidus to full hp, a wasted turn if you ask me and you also lose a turn later on due to Curaga's recovery time.

Without BHPL
Tidus dies (9,999hp) revived by auto phoenix, he now has 4,999hp, you can easily use quick pockets to heal him to full hp, you don't lose a turn later on.
Also if he is brought below 50%hp, auto-potion (x-potion) will instantly heal him to full hp, without wasting a turn.

So which of these ultimate armours would you now choose;

BHPL
Auto-phoenix
Auto-haste
Auto-potion//Auto-protect//Defence +20%

OR

Auto-phoenix
Auto-haste
Auto-potion
Auto-protect//Defence +20%