Lore reason or gameplay reason? Because both have answers.
Lore: We've stretched our own aether so thin that we're literally unable to attune and conjure another egi. A trance is the next best thing since we're taking that essence unto ourselves, and it's not like "oh, allagan summoners could summon whatever they wanted" because they couldn't, and the trance IS an allagan technique. Maybe in the future we'd get a Frost Trance, or a Levin Trance or whatever Alexander's title is, but for now we've spent so much of our aetheric reserves on giving shape to three mini-primals.
Your BLM argument is kinda flawed since Black and White Mages taking aether from the land was a direct cause of the flood that ended the War of the Magi, the consequences were that both Black and White Magic are now highly regulated and carry great stigmas with them. It is forbidden that any non-padjal use White Magic (with the exception of the WoL) and Black Mages were hunted down for the damage they could cause themselves and the planet. Not to mention that comparing archinima (which the modern summoner IS, by using an aetherial construct made of our own aether instead of crystals) with thaumaturgy (using the astral and umbral cycles) and conjury (borrowing aether from the land) is like comparing apples to oranges.
Gameplay reasons:
The devs know that to make the game balanced, they had to shift out the emelental wheel, making the resistances pretty useless. Maybe if the summoner had come out in 1.0 there would have been egis (since the plot line of primals draining the land of aether was from all the way in 1.0) from all six elements, making SMN a CNJ/pet hybrid (the 1.0 CNJ, which used all the elements). However, in 2.0 onwards, having 6 nearly identical pets whose only difference is the elemental damage they deal is redundant and a waste of already low resources; so, the trinity of melee/ranged/tank enters, make one pet useful for one thing. Unfortunately, that writes the devs into a corner: if a new pet is to be released, how do we justify it? what is the thing this pet has that makes it viable? Also, if the most of the DPS is on the pet then we go into the FFXI loldrg area. Lose your pet and you're useless until you can get it back.
Honestly, outside of making 4.0 into a "Oh, look, ANOTHER CATACLYSM! LET'S CHANGE EVERYTHING LOL" SMN is not going to change that drastically. Maybe 4.0 will actually give us a new egi, maybe it will allow us to do a Shiva/Thordan transformation WITHOUT it draining away all life on Hydaelin every time we need to stop the newest world-destroying abomination.