Balance is mostly a numbers game. The rest goes with ensuring the ideas match the numbers generated by the other classes, or that the tradeoffs are worthwhile for whatever advantage/utility those provide.
Except that when you have to turn a pet class into a non-pet class to make it "stable", that underlines severe issues with the design of the battle system. And that's not a good thing.If you look at 2.x, by the end of that patch cycle summoners were the weakest class bar none. They complained a lot then, and back then they actually had a good reason to, as well. It got fixed in 3.0- sure, they gravitated away from a conventional "pet class" some, but mechanically, they became much more stable, to the point that at 3.5 they are the most played class in the game according to the census. While mechanically, they feel less like the idealized version of a summoner some people want, the class is now arguably the most mechanically stable while still fitting into the lore reliably. If you want to change that, you should bring more to the table than "It's not what I want" and "I want more".
Just because something looks good in the damage meters does not mean it is soundly designed.
Again, balance is a numbers game. Concepts are simply to put together; the tricky part is making sure the numbers come out comparable to other classes.Your ideas(And thank you for bringing some to the table!) are nice, but can make the class a little too bloaty. You can't have one class do everything- which is why there's no healer egi, and only three egis. You put more in, each role becomes more niche, and balance becomes more and more of an issue.
If we made Shiva-egi a primarily crowd control egi (channeled CC to mirror the WoW warlock's Succubus), that egi is not going to be hitting hard compared to Ifrit when it comes to melee. It's edge would be the ability to crowd control, which could prove useful both in PvP and PvE encounters that make it grant your raid an advantage (also, instead of putting in a million memory games in raid fights, they should start adding adds that need to be CC'd or kited; not only would this give Shiva-egi a purpose, but it would also make Sleep and Repose no longer be wastes of space).
Leviathan-egi would also be an excellent candidate to mimic the Felhunter as an anti-caster pet. This means it'd be the only pet with the ability to reliably interrupt spell casts and weaken casters in general. We already have a template with what Levi does during the fight, with stuff like Gyre Spume being a debuff you apply on enemy casters to drain their MP/weaken their Magic Attack. Spinning Dive would be your interrupt on a 30s cooldown. Its overall DPS would be decent, but still behind Ifrit because of the ability to debuff casters. Much like Shiva-egi, Levi would be pretty useful in both PvP and PvE since you could make SMN part of an interrupt rotation if you decided to bring a DRK and WAR to tank a raid and only had 1 BRD, but needed a second person to help interrupt enemy spell casts (by the way, the devs should also add spells that need to be interrupted for raid fights).
If you have all your bases covered, Ifrit would still be the go-to DPS pet, but there's something to be said for having some flexibility in giving your group options for a comp. it wouldn't be a new idea either, since Warlocks used to have a buff called Demonic Pact that increased the HP of the raid when they had their imp summoned. The amount was comparable to the priest's Power Word: Fortitude, and was there as a back up in case you didn't have priests in your raid.
Having two classes that are conceptually the same thing is a true waste of resources.Really, to make them more prominent at all they'd need a complete overhaul and the class would need rebalancing to not be nearly as strong on it's own. It's also bound to Scholar due to the dual nature of the Arcanist class, and that can't really be stopped.
By that point, isn't it easier to just start from square one, and request something like an "evoker" class?
While I understand developers don't like rebuilding something from scratch, sometimes it's the only way to get a cohesive design and at least show a clear direction for the system in question. If SMN/ACN/SCH wasn't such a mess, sure I could say "leave it alone", but between the lacking implementation of the job crystals (because either the SMN crystal or the SCH crystal should be notably changing ACN baseline abilities to meet each job's needs) and the schizophrenic design behind SMN, I just point at the drawing board and say "redesign".