let's say they use the system a la FF11 here, meaning you simply give order, you don't need cast, since....well you only commanding the pet, meaning you can deal damage while moving, while being at distance. for balance this you need to make the pet deal less damage or loose the partial resistance to AoE. the first will simply make the summoner a bad dps and no one will want it and the second is clearly impossible with the lag and the time of reaction of the pet.... let's say they will die all the time.
the point to not have a summoner that simply command a monster is done because it will be either boring and a pain to balance and make it work.
they did decide to go along the way to add dot, for the good reason that while we try to control the pet a bit, the dot still do damage, we are not totally doing nothing. the dps is almost divided for 1/3 between the direct attack of the summoner, the dot and the pet. now they did added the trance for increase the damage of the direct damage and the dot of the summoner. they have a good gameplay, you did wanted a full pet class with nothing to do exept order you pet, i can understand it, but in all honesty, this in modern mmorpg is simply close of impossible.
like said before FF11 and FF14 are mmorpg, pet class in mmorpg need to be like this.... you can't hope to see simply the summoner unleash the hell on earth, it will be simply a glorified black mage.
10 and 13 are.... please don't launch me on this two i will become quite rude, since i think little good of this two one. for me they was the most bad of the whole series, don't get me wrong both had stuff for them, but they was soo bad in comparaison of previous episode in terms of gameplay and immersion that... well i prefer ignore them and i know some think that the 10 was one of the best.... (i can't understand how is possible *sighs*) we do have two Final Fantasy that are simply glorified corridor, until you reach the last part of the game, where finally you can explore the world, no real freedom.
anyway, each FF try to change the game in a way, but since the 13 is copying a loooooooot the 10 is normal that the system feel similar.
you know what i even prefer the system of summon of FF type-0 to the one from FF10 and FF13. that said...what you do in 1 player game and mmorpg are not the same trying to copy what you can do from a solo game while allowing player to play together is... a no no.