The body does need to be in shape, and the mind does need to have those connections to the body.
It doesn't train the mind to interprete music, or necessarily to read music, and it's not actually learning lit.
If it's "bad" then you're doing something wrong. It's something effective enough to produce a result though (although a bad result). Just tweak it or ease off and get good results.
Playing with you're brain means thinking, playing actual literature, interpreting and feeling the music.
I'm thinking more along the lines of just pushing your speed ability to play a scale. If you can't play a scale at a certain speed, you still won't be able to play it in an actual piece of music, and with actual music you have lots of other things to think about rather than plain technique.
I don't see anything wrong with either way, whatever your goals are and whatever you can stand. I don't really like "weak" etudes, the ones by "lesser" composers that you never hear much about. What's the point of drilling yourself on someone else's lesser material? I like tech exercises that are more plain than etudes anyway. More focused things. A lot drier than any etude I've seen, but still more efficient at producing results. At least for me.
I don't know what that piece is exactly and I'm not going to go check it out.
I wouldn't bother writing anything out if you just want the physical technique.
Just break it up in chunks. Identify what technique it is. Transposing exercises to all 12 keys (at least 12 on the keyboard) is an easy way to expand things.
If it's scalar, practice scales and finger patterns to get your fingers moving faster and better over scale patterns.
If it's leaping, practice leaping. Make larger leaps. Whatever you want.
Alhtough, this is a very global approach. I consider it stamping out that problem for that piece and any other situation in a piece like that.
And it takes a lot of effort and time. Careful pushing and backing off and easing things. Daily over weeks. And then seeing results in a couple weeks and really solid results after six months or so. It depends how well you push and can recover and restart everything.
And it's possible you're just using the wrong technique or playing to tense or something. If you've got a fingering that makes it really difficult, than pushing self like I described above might not help much. Not if you can just use another technique and get it.
And take everything I say with a grain of salt. My playing is probably only solidly intermediate. Not method book intermediate, but intermediate/early college level. I wasn't making much technical progress with lit, so I started doing tech exercises because they worked. Solved a lot of problem and worked a lot better than lit, but it meant I was playing lit though either. It's a toss up.
I still don't know what to think about "things just happen." They didn't for me. I got better results getting the body working on easy-to-understand material. I don't know what child prodigies are doing, maybe just born with better dexterity otherwise everyone would do that. I have seen plenty of pianists with heavy forearm muscles hanging down and pianists with golfball size pinkie muscles -- the muscle on the hand that moves the entire pinkie finger down toward the palm. Literally the size of a golf ball. I can't believe that didn't take some stress and recover to develop or that it magically appeared because the mind understood the music, or that having a developed muscle wasn't either very nice or very necessary to play difficult works.