On SMN, I don't mean the visuals at all, actually. You have Ifrit's long casts and required melee range, Titan's total freedom of movement, or Garuda's mostly freedom with a VERY long cast. SMN is a DPS, so doing damage is what it's going to be. Much as I'd love having Summons to deal with different situations, I don't want SMN being made a Limited Job to get that.
My point was not that.
My point was that you have a rotation, but it's not rigid. Contrast DRG with SMN. The former is absolutely rigid. Buttons are essentially pushed in the same order more or less no matter what because of how its rotation works and how rigidly it flows between attacks. On the opposite end, you have something like BRD, which has no rotation. It has a priority system based on what's procing, an underlying long rotation of the songs, and then a filler attack for when nothing on your higher priority system is up/proced. SMN kind of straddles the line between these extremes, having a rotation that has waypoints of rigidity (Bahamut/Phoenix), but between those points has flexibility in how you get there.
I get it's easy to miss that if all you see them as is "damage vs damage", but...it's a DPS Job. They ALL are "damage vs damage" when it comes to their core rotation. Vercure is not part of the core rotation. RDM's buttons are also all "damage vs damage". That's the way it works due to the rigid combat system FFXIV has, so that's not what I'm talking about.
I do also disagree with your "non-FF players notion of..."; Summoners have been distinct across the history of the games to the point that isn't really a valid point. Sometimes even within the same game. Contrasting Garnet and Eiko's Summoning in FF9, for example, the latter has an array of support Summons and several uncommon elemental attack summmons (like Wind and Holy) while the former has mostly just direct attack summons which are more powerful. The attunement/augment effect of EW SMN also is vaguely similar to FFXVI's Clive, though in a pure caster form rather than Clive's hybrid caster/fighter form.
...the point being, FFXIV's SMN is distinct, as all FF game SMNs are, but well within the realm of what a Summoner is.
Pre-EW's SMN was not. You focus only on the mechanics (and only vaguely at that; Phoenix in EW and ShB is vastly more different than Ifrit and Garuda and Titan were from each other in ShB, for example) but I think that's why you miss how EW's SMN feels more like a FF Summoner to people. Pre-EW's version had a heavy focus on DoT gameplay (something Summoners in FF games...don't have; I can't actually think of a single one offhand whose primary gameplay revolves around DoT maintenance), and the Egis didn't feel or work like any Summons in any of the games other than maybe the one Tactics with Vann and Penello in it. No other iteration of Summoner that I can think of had a permanent follow-pet. The closest might be FF12's, but they were temporary big attacks (costing a charged resource to use) and ended with mega-attacks, which the Egis did not.
I can't think of a single FF game where the Summoner played like pre-EW's SMN did.
I think this is what most pissed me off. I don't mind it having the same general animation as Ruin 1/2, but they didn't even give the little flying ball a red/green/yellow tint. you can't even tell if you're casting the elemental one or the normal one, visually.