I don't mean to nitpick, because you're right that Bladesinging isn't trash--when I say it doesn't offer anything not available through multiclassing I mean it doesn't fundamentally change the paradigm. I obviously don't mean that you can get those benefits for free otherwise.
But, here's my response to your point-by-point:
With life cleric + enchantment you have -10 move speed (or -feat), -1 spell level known, -1 bump progression, -1 feature progression, and a 13 wis requirement. You can use shields, but your build is not going to really allow you to make opportunity attacks unless you also take warcaster, so you are likely just sitting in the back like a normal wizard.
The MADness is, in practice, the biggest limitation. If you roll only a few decent stats you will usually want to go Fighter 1 instead of Life Cleric 1. The movement speed is offset by either Mobile feat as a variant human (which has other benefits as well--although for a tank, Warcaster might be more desirable, depending on how you plan to play), or the Longstrider spell or Expeditious Retreat, or by pumping Str to 13 or 15.
It's more like -0.5 spell levels known since you're only behind 50% of the time.
In return you gain bonus action no-concentration Sanctuary for even better tanking, access to Bless and/or Shield of Faith (to taste), secondary healing capabilities, and potentially better healing on Vampiric Touch (depends on DM ruling). It's not a clear dominant option, but neither is Bladesinger. That's what I mean when I say it doesn't fundamentally alter the paradigm. By 5th level you can either be an AC 20ish Bladesinger (plus Shield and/or Blur), or an AC 21 Fighter 1/Wizard 4 (plus Shield and/or Blur), or an AC 20 Life Cleric/Wizard 4 (plus Shield and/or Blur and/or Shield of Faith and/or Sanctuary). All of these are very tanky options and likely to perform similarly. The difference is that the Bladesinger is slightly ahead on wizard spell levels in exchange for having none of the regular wizard goodies that come from specialization.
With bladesinging (starting at 16 Dex) you get about the same AC as the MC twice a day along with BONUS move speed, enhanced concentration checks, no spell progression or feat progression penalty, and no wisdom requirement.
It's twice per short rest actually, which highlights the point that the Fighter/Wizard or Cleric/Wizard will have better AC the rest of the time, including on the first round of combat before spending a bonus action. That may or may not be significant depending on how fights tend to happen at your table: how long they go, how much warning you have, whether you get to rest frequently, and overall how far your table leans to Combat As War vs. Sport.
So, Bladesinger has more mobility, slightly worse AC until mid/high levels, comparable ability score requirements (Enchanter: high Int, mid Str/Con/Wis) vs (Bladesinger: high Int, high Dex, mid Con), enhanced concentration checks while Bladesinging, and +0.5 max spell level.
Bladesong vs Hypnotic Gaze
Bladesinging offers a whole host of benefits that work perfectly well from the back row where you want to be when chucking around your spells. Which is what you will be doing on most turns anyway. Hypnotic Gaze is good, specifically when you have very few spells, but I think its pretty clear that on a head to head comparison Bladesinging is more useful in general.
As mentioned previously, the whole reason for taking the Life Cleric/Enchanter combination is if you want to be the party tank while still being a full spellcaster. If you plan to hang out on the back line I'd recommend something else entirely like Necromancer or Illusionist. Bladesinger is a defensible choice for a back-line caster, but unexciting.
But if you actually are a front-line tank, you can be making your enemies hit each other every round while you hold down another enemy with Hypnotic Gaze and possibly yet another with a Grapple. Possibly two more with Tasha's Hideous Daughter^H^H^H^H^H^H^H^HLaughter.
Advantage: Enchanter
Instinctive Charm vs Song of Defense
As you said Instinctive Charm is incompatible with shield, and far more situational, requiring specific positioning.
Song of defense, on the other hand, does not interfere with shield, because it can be used on any damage source, including the most dangerous ones in the game, such as dragon breaths.
First of all, why are you comparing Instinctive Charm (6th level) with Song of Defense (10th level)? At 10th level the Enchanter gets the ability to twin Hold Person/Monster for free, among other spells.
Song of Defense is okay against critical hits, but it still competes with Shield (costs your reaction)
and competes with Absorb Elements (also costs your reaction). Instinctive Charm, Song of Defense, Shield, and Absorb Elements all draw upon the exact same action resource so you cannot credibly claim that it doesn't interfere with Shield. Of these three, Instinctive Charm is the weakest defensively because you have to declare it before you know whether the attack would have hit or miss; but it's also free and can/should be used frequently. Song of Defense will probably protect you about as much, over the course of an adventure, as having somebody in your party with the Inspiring Leader feat. It's not garbage, and it can save your life in the right circumstance, and if it weren't for Absorb Elements it would be rated a lot higher, but overall it's solid, not terrific. Suppose you're facing a couple of Young White Dragons at level 10, and they both breathe on you. Absorb Elements (Cold) with a 1st level slot will cut damage from 70-90ish to 35-45ish. Song of Defense with a precious 5th level slot will cut damage from 70-90ish to 45-65ish. Really it's hard to imagine a dragon fight where Song of Defense is appreciably better than Absorb Elements, unless I'm overlooking a breath weapon type that Absorb Elements doesn't work with.
Again, Bladesong isn't garbage, but it's largely redundant.
Advantage: Enchanter
Split Enchantment vs Extra Attack
Split enchantment is definitely better than extra attack for an enchanter, and extra attack doesn't add that much for BS.
However; let's look that the spells you will probably use this on: Tasha’s Hideous Laughter, Hold Person, Hold Monster, Otto’s Irresistible Dance.
Tasha's: Good!
Hold Person / Hold Monster: good but, you could get the same effect by just using the spell in 1 slot higher.
Otto's: Eh, you are only going to use this on legendaries, probably. And hopefully you aren't fighting two of them.
Split Enchantment is better but it's not the be-all-end-all.
Advantage Enchantment
Again, it's kind of weird to compare a 10th level feature vs. a 6th level feature, but my assessment of Split Spell generally matches yours: it's good, but not a killer app. About on par with Song of Defense IMO, although you can leverage it to better. (Significantly, Hold Monster VI is a
lot more expensive than Hold Monster V because it eats into your precious 6th+ level slots. Note: I play with spell points at my table, which makes 6th level slots even more rare and precious, so I may have an exaggerated view of the gap between 5th and 6th.)
Song of Victory vs Alter Memories
Song of victory is generally speaking better than alter memories, unless we want to get into flavor and RP discussions.
Advantage Bladesinging
Eh, I can see it either way. Neither one is especially exciting except in the context of a specific situation. SCAG cantrips are already competitive with Bladesinger damage using Song of Victory; and if you're playing either a backline caster (as you suggest above for Bladesinger) or a Mobile Warcaster Enlarged grapple-tank (perhaps the funnest way to play an Enchanter tank) you're not likely to care about melee damage anyway. The only case where Song of Victory is actually good is where you're enjoying being a melee gish for the fun of it, because you don't like cantrips, which means it's more flavor than anything. And it comes really late in the game too--at this point you've already got Simulacrum!
So taking life cleric 1 for survivabiliy and then going enchantment is a perfectly valid choice. In fact I would call it a strong choice. If you want to be an enchanter, then go for enchantment. It's very good. However, i think that because bladesinger's abilities are more broadly useful, it gets a higher rank.
Thanks for explaining your logic, and thanks for the discussion. Your ranking of Bladesinger is valid; I just wanted to point out some things for the sake of other thread readers.