While I most certainly wouldn't shake a stick at more damage; I cannot help but disagree with the comparisons being made... "Automatons are doing 2-5k max"... "Summoners are doing 15-99k damage"... "BSTs can spam tp moves at a higher purpose frequency and they do more damage"...
I think it behooves us to analyze this request a bit more thoroughly... Puppetmasters (PUP) use an Automaton which is customizable... bst and smns pets are not. PUPs Automatons can reliably tank Notorious Monsters (NMs) (when proper attachments are in place)...NMs which bst and smns cannot reliably tank... PUPs can heal literally an entire party of PCs/Trust party members, where as a bst and smn pet cannot (at least to the same degree)... PUPs can rapidly and reliably skill chain not only with the Master but with any other party member performing a corresponding weaponskill to which their attachments allow for a skill chain reaction to be performed... smn and bst (although can do this to a certain extent, it is mostly the realm of the PUP)... PUPs can use regeneration of the automaton's hitpoints to reliably keep the automaton alive without the need to spam "oils".... bst and smns healing potential of their pet is extremely limited....
The damage output associated with PUP is directly tied to that of the Master; as such, and in my opinion, I do not believe we are doing the job itself a service by comparing the damage output of BST and SMN to PUP in relation to the "amount of burst damage" both BSTs and SMNs generate with their pets at end game... compared to that of the PUP.
I also believe that making such adjustments wouldn't benefit the job, as it would turn into the same type of "send in pet without master to perform burst weapon skill on enemy"...but considering the degree in which we would be able increase defense as well as hitpoint regeneration of our automatons, such scenarios would tend to be broken... Possible reason why BST was adjusted to have them be so "close to their pet" to heal them with a biscuit.
Saying all of that... I do not believe the request as stated, is justified.