Overall I agree with the point you are making, but I don't really agree that "it was designed to be played" in any particular way. Bethesda makes a point of making the console relatively easy to decipher (and so much so, that they project extending that functionality to console gaming platforms) and that just doesn't fit with what you are suggesting: that the game was "intended" to be played with highly canolized play styles, i.e., "in-character" play throughs. The other thing is the openness of this game (and all of them since at least Morrowind) to being modified with user content and plugins. They are happy to let you play the game HOWEVER you want to play it, as long as you do not breach the EULA! 
In sum, it was almost assuredly "designed to be played however the end user chooses to play it" although with some 'suggestions' and nudges in some particular directions that they think might be most edifying for a large segment of users (particularly those new to the franchise, or to games in general). Its called "good branding" or else "good marketing" and Bethesda have shown themselves to be masters of it and we should all thank them for the incredible value we get out of their products as a result of this specific type of design.
There is nothing at all "wrong" with strict "in character" play style, in any game really, single player, multiplayer or coop (well, it might get real annoying with some coop groups and you might find yourself locked out of the Teamspeak channel
) but then again, for a single player game there is nothing "wrong" with doing anything you want to do as long as it doesn't breach the EULA.
I myself was first a historical military strategy gamer, and second a D&D player. I can enjoy some good "in character" play, but even in the groups I've played with where that was mutually encouraged, there were frequent shifts into "strategic optimization" mode!
After all, if you invested hundreds of hours into a character that you really get into and enjoy the last thing you want to do is have it get killed because the DM or the game put you in a situation where doing something that was wise and self-preservational was mutually-exclusive with "being in character." Indeed, I would say that, in some campaigns I've participated in, as much time was spent discussing the tradeoffs between these two imperatives (being "in character" versus "doing the wise" thing) as was spent making progress through the game world!
The other thing with computer games is, the rule systems, the "ecology" as I call it, the invisible boundaries, hierarchies and forces that govern the game world are best understood by trying different things. For example, by virtue of engaging in a long play through of out-and-out min-maxing (but without any use of guides, wikis, or any other "meta-gaming" crutches, etc.) I was able to have several hundred hours of fun, died only once and now have a level 74 character that is Godlike. Not exactly "game over" but not exactly fun anymore either. No regrets! I loved it!
Now I can go back and do it a different way, and again, and again, and again.
Just keep in mind, the OP expressed confusion or incomplete understanding of how it is that some of us say "the game gets too easy at higher levels," so some of us who have had that experience have been explaining what we think accounts for it. You are correct that, part of it is "our fault" but it isn't really "faults" so much as it is "cause." You can handicap your character however you want and as a consequence face death more often (and thus either, run away, expend damage mitigating resources or die more often), or you can anolyze out the wazoo, throw "in-character" out with the baby and the bathwater and avoid damage, risk and death progressively as you level up. The choice is one each of us makes whenever we play, but if you don't understand how to do the latter and are asking how it is even possible it might be helpful for those of us who are good at the min-maxing approach (or whatever you want to call it) to explain how it is done.
I don't even think that making the decisions one makes in the course of a "min-max" play through are necessarily that "out of character" for any but the most irrational or dogmatic of "characters." Most humanoid entities want to survive as long as possible and if you try to imagine yourself, or most sane individuals, in the situation the Sole Survivor faces as they awake in Vault 111 I would argue that "most" of the min-max decisions are simple common sense.
You know that:
1. There was a long drawn out war between your country and China
2. Nuclear apocalypse was largely regarded as inevitable
3. It happened, and now you find yourself awakening after an undisclosed period of time inside a vault, underground near your hometown.
4. At some point in the interim, your spouse was killed and your infant son was kidnapped by some "strange" looking people.
There are real people who think in these terms and have shaped their entire lives in anticipation of this sort of eventuality, they are called https://en.wikipedia.org/wiki/Survivalism. Most of us probably don't think and live that way in normal life, and you raise a good point that: many of the characters we might be portraying when we enter teh vault probably also would not be of that ilk.
But even BEFORE you exit the chamber with the frozen cadaver of your deceased spouse, you have already faced enough evidence that most sane and resourceful people would already be shifting their mindset in the direction of survivalism I think. It sort of doesn't make sense that anyone would emerge from the vault the same person as when they went in and if anything an overriding sense of "I need to figure out just how harsh and deadly this world really is now and what I need to do to survive it" would tend to undermine and antecedent character elements that contradicted such a cautionary and preparatory perspective.