There are a couple of problems here.
The primary reason we don't have balanced sets has to do with string mass, which is a function of material and diameter. It is why, for example, we use nylon trebles and wound basses.
On Steel String Acoustic guitars you may notice the G is wound - and this was actually true of Electric Guitars in the 60s until rockers started using thinner gauges and putting plains on the 3rd string slot.
In order for a string to operate effectively, it needs to be near or at its breaking tension.
But given the tuning we use - which makes a secondary reason - that tension and string diameter/mass means a certain "mass-to-tension ratio" works best.
Just for example, a plain 3rd string 18 gauge tuned to G does not behave properly compared to a wound 3rd string 18 gauge tuned to G because the mass of the strings is different, and thus a different tension is on each to tune them to the same pitch.
So generally speaking, strings have evolved such that the mass and tension works best for tuning to the notes we tune to (or typically tune to given other possible tunings).
So while a "balanced tension set" seems good in theory, it usually has the side effect of some strings being too "thick" or "thin" feeling under the fingers.
I do know there was someone making Electric strings in a "balanced tension set" but they've not taken over the world.
Of course guitarists (electric or otherwise) tend to like tradition and are slow to adopt new ideas, but I think the issue is one of "feel" with diameters - it just doesn't "feel" right.
Now, I agree - it kind of drives me a little crazy that the B string on my electric is way easier to bend then the high E - I can bend the B a step and a half with no trouble, but the E I can only get a whole step out of it without really killing it. So the B does feel a bit "flimsy" in comparison.
But there are some instances IIRC where if you go up a gauge, the tension increases dramatically so now it's too high for the set.
There used to be an online string tension calculator using the tensions D'Addario put out. It was just an Excel spreadsheet but worked great. You put in the gauge, type, and tuning (I think it even had scale length) and it would tell you what the resulting tensions would be.
I played around with it a bit looking for balanced tension (on electric) and it was something a little odd like 9.5 as the high E. But that was way lower than I wanted to play (I play 11s on electric).
I know Nylons and Silk Wound strings are different, and there are additional ways to increase or decrease mass in a string to alter tension characteristics, but I think for Classical you would basically end up with what is a "mixed bag" of strings.
I have read here that people like Segovia would often play a melody line in a piece on a certain string to give it a certain character, and it almost makes sense that the high E could easily be a "chanterelle" string - something different to make it stand out.
But that sort of plays off the natural character of the "normal" 3+3 set.
You're almost there it seems - roughly the same basses, the same B and G, and then a different high E - could be your "melody" string if you wanted that sound for anything on that string.
I'd say though, if it works for you, go for it.
I think a lot of players get used to the gradation of thicker to thinner in 2 sets of 3, and the G-B-E set feel roughly like a "repeat" of the the lower 3 (on acoustics and electrics it tends to feel like a continual decrease).
So for them, the feel of a suddenly thicker or thinner string "out of order" maybe throws them far more than than the tension differences.
I have often wondered about tension differences on the structural integrity of the guitar, but given they've been made for decades or centuries this way, seems to be of no major concern.
But, if balanced tension sets could be had with the right diameters for "feel" and then the right mass-to-tension ratio for tuning, I don't know if there would be any observable improvement other than as you say - a "flabby" string (would be a bigger deal for bending styles).
Still probably a hard sell unless they sold them at lower prices...and that probably wouldn't happen!