FE Fates has its issues, but it also introduced us to the talisman magic. The whole concept was summoning spirit-like creatures to attack the foe. It already lines up with site lore nicely with magic working via the respective spirits.
It would be a large change but I propose the additional school of magic. Or, a potential alternative method is it could count as an exotic weapon exclusive to magic users, as they summon a creature for their respective school.
We have already seen Hargus summon creatures of Nether, thus began the Arum plot, and the second half of Hero City. So why shouldn't the average player be capable of something similar? The creature should start out respectively simple like the rat talisman and grow as the mage does.
As for the why has it not been seen? Two easy possibilities, it developed on Vinland, where beastmen roam and mages used magic that immitated them, or it is just a niche thing so not often seen.
While I am neither arguing for or against this, I would point out one thing concerning Hargus. His summoning abilities were brought about by a dual combination of absolutely monstrous power(arguably still the highest power seen in the sights lengthy history) and very advanced magic through a forbidden and very special tome.
Simply an answer as to why Hargus could as opposed to the average person. Though I can say that the mods often talk about what to add or what not to and your points will definitely be brought up.
That is a good point on Hargus, and I really should not have used him as an example in the way I did. What he did was some next level stuff and he did mass summoning. I mean its doable in lore now and I feel we should be able to have some toned down capability.
In all honesty, the Talismans of the game can already be effectively mimicked here by normal mages. There's no rule saying your fireball CAN'T look like a rat or an ox, and the talismans in the game similarly followed very linear paths - if you use Fimbulvetr, it doesn't really matter if you throw ice shards or have frozen rabbits charge the foe, the end result is just a spell that does damage. You could make a fair argument that a 'shaped' spell is harder to cast than a normal one, but if the mechanics are the same I don't see why it'd be a a huge deal.
Summoning things that actually have intelligence, who can act on their own and track foes or stick around, is something different entirely, and not portrayed in Fates' Talisman magic.
Somewhat similar to Remus's post - not a strong argument for/against summoning - but if all you really care about is "I want my fireball to look like a bird" you can already totally do that!