If you ignore every version of Summons after IX, sure, that's the case. Mostly due to hardware limitations. Though I'll note some of the versions I'm glossing over did more damage based on you letting them play their animations out, which technically has elements of ghosting in it in that both are damage losses. I think wholly disregarding X through XIII is big blow against this argument though, as all of those games had Summons act as individual party members once summoned, and X, like IV, VI, and VIII before it, featured them as a major point of their plot. Keep in mind that that argument also applies to Beast Master, which everyone also thinks 'should' be a pet job on the mere distinction of Fantasy Monsters vs Fantasy Demigods, which basically boils down to Mundane vs Magical at the end of the day, and also does not even feature in any main series game other than XI along that split. XI is indeed a major influence, but I'd argue if you think SUmmons shouldn't be pets you should think Beastmaster shouldn't get them as well.
Basically, that particular argument is dubiously applied at best. Summoner can be however SE wants it to be. We all can agree they decided to reneg on pets because they couldn't get the AI to work responsively enough for players to be satisfied for a decade, which I can still think of reasonable solutions for (adding charges to pet auto-spells, allowing their AI to be made asynchronous like other mechanics to account for the hardlock issue, and enabling the devs to update their priority list to actually prioritize player input properly). That's not what they decided to do though. They're cutting their losses. If they'd at least kept autos around on Carbuncle I think I would've been happy with it. I would have been much happier if they actually upgraded the Egi graphics instead of going for this lazier route, as it's where 90% of the actual complaint was (Pick any SMN complaint topic, you'll find it on the first page unless the OP said some batshit stupid nonsense). If they had wanted to, they could have put this same animation work into the pets as they were and it would have paid off considerably. Alas, they couldn't be bothered.
And if Demis are still on /heel AI I'm gonna be pissed. Just let us use /place like normal people.