Theoretically that's true.
What is theoretical about it? Why wouldn't a 4E stat block include the key skills of the enemy, the weapon and tactics they use, character-specific bonuses and their ability scores?
But the point is that 4th Edition's monsters were explicitly designed to support 5 rounds of combat and nothing more. (We know that because the designers told us it was true.) Those same designers who said "monsters are good for 5 rounds of combat and nothing more" are the same designers working on WotC's modules.
Shockingly, the opponents in these modules are good for 5 rounds of combat and nothing more.
Look, that's a complete misrepresentation of the designers' views. The approach they set out for, in 4E, was to include the information for monsters and NPCs that was relevant to their role in the game.
This means that if an adventure has a wise old sage you can ask for advice? It will likely include his ability scores, skills, and any rituals he can cast for the party. It won't include combat stats because, no matter how smart he is, if the PCs want him dead they'll just kill him. You should neither need to have the DM waste time statting those elements out, nor an adventure waste space listing them.
The condensing of combat stats in the 4E stat block is built on the same philosophy. Namely, that monsters don't need a list of twenty abilities that will never be used in battle. That doesn't mean they don't need personality, nor does it mean they shouldn't exist out of combat.
I ran H3: Pyramid of Shadows. An adventure that many criticize as simply being filled with one combat after another. Which can be true. But it also has plenty of room for those monsters to come alive outside of combat - there are various factions the PCs can work with (if they desire), and NPCs they can interact with.
In my game, they recruited one NPC as an ally (until he inevitably betrayed them), and hired others as mercenary guards rather than fight them. They were tricked by a succubus into freeing her from the pyramid. They dined in a village of far realm cultists, and joined forces with the spirit of a dragon to close a rift to the far realms.
They interacted with the mocking sendings of the main villain, and unravelled his past through dreams and books found in the pyramid's library, and the entrapped spirit of his dead wife.
And this is a group whose typical approach is to simply hack their way through everything. There was plenty of room for a more intrigue focused group to play the factions against each other in a far more elaborate game.
None of which was somehow made impossible due to stat-blocks slimmed down to be useful in combat.
To reiterate: The problem here is not that Premise A gave us Stat Block B and then Stat Block B gave us Problem C. It's that Premise A results directly in Problem C. The fact that Premise A also results in a flawed stat block which contributes to Problem C is practically irrelevant: The faulty premise, and every conclusion resulting from it, needs to be re-analyzed before ANY of the problems can be solved.
I don't see any actual support for your theory, though. What faulty premise? That stat blocks shouldn't have a dozen spell-like abilities the monster won't use?
Ok, I admit it - having a few more ideas of what a monster is capable of can give the DM more ability to adapt it to the different approaches of the PCs. If a monster can cast invisibility, fly, charm person, true seeing, and meteor swarm, it has all sorts of ways it can interact with the PCs.
And... 4E doesn't really change that. Monsters can still have invisibility powers, charm powers, flight, truesight and attack spells. The key is that they don't need another twenty spells, most of which are trivial. How much does it matter that they can cast Aid, Bless, Cause Fear, Entropic Shield, Inflict Light Wounds, Eagle's Splendor, etc, etc, etc.
Ok, having all these spells gives it a list of buffs it could provide PCs. I suppose. But those sort of buffs have largely gone away in 4E, anyway. You can still have a monster that can offer smaller bonuses or healing to friendly PCs, or perform rituals for them as well.
But you don't need pages of spell lists and spell-like abilities. You don't need your CR 16 angel to have "Use Rope +4 (+6 with bindings)". That isn't there because using ropes is a fundamental part of the character - it is there because they had leftover skill points, or needed to reflect a synergy bonus from some other skill, or something entirely meaningless to the actual NPC.
Look, ProfessorCirno gave an example of an enemy whose 3.5 statblock revealed all sorts of character information. I commented that pretty much everything relevant found in the 3.5 statblock would also be in the 4E version. You can't just dismiss that as theoretical.
If people have an issue with 4E adventures and the role of enemies within them, that is one thing. But saying that the statblocks are flawed at the core requires a significantly higher burden of proof. I'm seeing a lot of biased perspectives and false claims, but not anything actually demonstrating a problem.
Indeed, in my own experiences, the stat blocks - even the adventures themselves - have had the room for monsters to certainly exist "outside the battlemat". I don't imagine that is the case for everyone, but the claim that 4E fundamentally forbids this - or prevents it - simply isn't true.