I want to say, I'm really happy I made this topic and about those who have opposed my claims here, because it has been a real learning experience, so thank you all.
Blur is better than Mirror Image for anyone who has a high AC already. Blur + heavy armor + shield + Shield
So typically an eldritch knight who is okay putting one of his/her school unrestricted spell choice, his/her off hand which now can't be used to hold a weapon, a second level spell slot, a first level spell slot per round, and his/her concentration all toward AC. And who has the strength to wear heavy armor. Seems like kind of a specific build, if you want to be unhitable you could always through Mirror Image on top anyway. If you have heavy armor proficiency and Blur and are not the above, you must have gotten the prof from either a feat or multiclassing into being a gish wizard, which I don't see or hear of very often, so I can't really speak on. I will say though, that if you are holding a shield, it seems less likely you are using strength for damage and dex makes your mirror images disappear slower.
Blur + heavy armor + shield + Shield will let you tank a platoon of forty orogs (even if they set up a goblin conga line) or githyanki for long enough for your buddies to kill them. Mirror Image will have almost zero effect.
Given 5e action economy, how often do you face forty of something, much less forty of something that could hit you consistently enough that you would need Blur despite having a high AC already? Of those that hit, how long would it take for them to whittle down your hp? Is that amount of time shorter than the amount of time it would take to decimate the horde with, say, a fireball or other decent AoE?
In fact, I've been really disappointed with how Mirror Image works out in play. I initially thought it would be nice against single big monsters, especially because there is no concentration cost, but a couple of years of experience later, my main impression is that it's almost never worth casting because anything tough enough that it would be useful is likely to have blindsight or truesight and be able to ignore it. It's probably more worthwhile for lightly-armored AC 13-15 wizards of course, because their threshold is lower for which monsters are "tough enough to need Mirror Image against." But it isn't useful for gishes, and even the lightly-armored wizards are probably better off (IMO) just casting Expeditious Retreat and/or hiding.
This is true. It seems like it's very difficult to analyze how balanced things are for gishes, which explains how we got the bladesinger. Do keep in mind however that anything that can see through Mirror Image can also see through Blur.
I'm not gonna quote people here cause a lot has been said on the matter, but upon rereading Magic Mouth and learning that you can choose to have it persist after delivering its message, as well as hearing all the creative uses for it, I've been sold. Magic Mouth sounds really cool, and more importantly it seems like the way you use it is all about the power of preparation, which I feel is the central theme of playing a wizard. I had a few things to say about some of the uses people proposed, but the spell seems useful even after such considerations, and this has been a long post, so I'd rather go take a walk and stretch my legs. Thanks again everyone.