If BST are not meant to charm anything, and not meant to tank, (and obviously not meant to heal or nuke) then they must be a damage dealer. Every other DD job has a method of increasing their TP gain.
WAR: Double Attack, Retaliation
THF: Dual Wield, Triple Attack
MNK: Martial Arts, Kick Attacks, Tactical Guard
SAM: Meditate, Store TP, Hasso, Sekkanoki, Zanshin
DRG: Jump, High jump, Conserve TP
DRK: Absorb TP, Occult Acumen, Tactical Parry
NIN: Dual Wield, Tactical Parry
DNC: Dual Wield, Reverse Flourish, Tactical Parry, Conserve TP
BLU: Double Attack, Dual Wield
PUP: Martial Arts, Tactical Switch (and double attack/barrage/haste through it), Tactical Guard
PLD: Shield Mastery
BLM: Occult Acumen
SCH: Occult Acumen, Adloquirum
RNG: Velocity Shot, Double Shot, Barrage, Conserve TP
COR: Triple Shot, Tactician's roll
RDM: Shield Mastery
Only BST, WHM, BRD, and SMN don't have one. And only one of those jobs ever melees. Even the MAGES, who never melee have something.
I suggest one of (or more than one) the following.
A) Quadruple Attack as a trait. Even just 2% activation would be fine. WAR's Double Attack is 10%, THF's Triple Attack is 5%, quadruple attack at 2% would be in line. (and the ability to add 1% more per merit would be appreciated, like WAR and THF)
B) The ability to switch TP with your pet, or just take your pet's TP. Since most pets' weapon skills do less damage than a normal hit, or can only attack every 2-3 minutes (like Shasra) plenty of tp is wasted on the pet.
C) The ability to skillchain with your pet. Wouldn't increase TP gain, but at least the pet's TP isn't worthless, and the TP you do get is more useful.