For what it's worth:
I had piano lessons from the age of 7-10. I didn't practise as much as I should have, took no exams (I don't even know if my teacher did them) and learnt only the one-octave scales, single-handed, which had white keynotes.
My father was a musician but was away from home for two years and then we moved so that he could take up a school teaching job. By that time he had shown me how to pick out some chords to harmonise tunes I played by ear, so I enjoyed doing that, and I think my reading wasn't bad, but I had no good technique to speak of (I remember nothing at all being taught to me in that respect, but it was over 50 years ago!)
He gave me two lessons after we moved - I was sort of just sub-grade 1, I'd guess - and we squabbled all the way through them, it was like trying to teach your wife to drive, and he said he found me unteachable, and didn't give me any more.
Not piano, that is. He did teach me enough general musicianship in six months to get me through the LCM General Musicianship grade 4 with honours when I was 10 - so I couldn't pass a piano exam, but I could take simple music dictation and play you a plagal cadence in B flat.
I learnt the cello; I sang alto, at sight, in the church choir, where he was the organist; I took grade 5 theory, with his tuition, at 12; I busked through duets of Mozart Symphony arrangements with him; I sang Lieder and British songs reading over his shoulder at the piano. But no more piano lessons.
Meanwhile, as we had a front room with a piano and nobody else used it much, and there were always fresh piles of usually second-hand piano music appearing out of nowhere, I played for myself for about 5 years; I played hymns at Sunday school on the organ and on the piano in school assembly - at 14 I wielded great power because I feared flat keys, never having learned them, and transposed tunes in E flat and A flat into E and A, thus making the whole school sing a semitone higher
and I composed songs and anthems at it.
I played for an average of about 90 minutes a day. I could read anything. My fingering was dreadful, my touch was thump and I never did any scales.
I took a very early A level (15) and as it was then decided I would try for university eventually, we thought I had better get back to having lessons again. My teacher put a Mozart sonata in front of me and read through it, well enough to show that learning it would be no problem.
It's a grade 6 piece, she said, you could do grade 6, you have grade 5 theory (actually I think by that time I had grade 7 or 8 theory and was working for grade 8 singing)
"Now are your scales?"
Non-existent. Luckily in those days it was assumed that if you were doing grade 6 you'd already learnt them in all keys so you only had to offer one group of three keys. We chose the "simplest" group.
The first week I had to do C major ONE octave with both hands going the same way. I'd never done it! I thought it would kill me.
Week 2: three octaves. Put my thumb under my FOURTH finger? Do people do that?
Week 3: C minor, harmonic AND melodic. I could write them with no effort. Never had to play them.
Week 4: E major AND both minors. Groan, sob.
Week 5. And 6, 7, 8, etc. A flat major. Start a scale on a black note. I thought I would never, ever master it.
I did, years later, actually learn to love playing scales on the piano.
Meanwhile my fingering was rationalised and my touch improved as I was encouraged to listen to myself better. I played in a lot of festivals and never ever got a good mark for solo work, though I got on well in duets and accompanying.
I still played for enjoyment, though I suspect the amount of "practice" I did was less than I was doing when I wasn't having lessons. It was always my second study anyway, my first being singing.
I don't think my time away from lessons did me any harm - perhaps if I wanted to become a professional player at an early stage there were one or two finer points of technique which were missing, but mainly I was using the piano as a music-making device.
My only other lessons, once I left school, were one year at the RAM, after I'd done my degree, with a teacher who only ever got to teach second-study pianists. I failed my piano exam (oh the shame) but learned heap more about technique.
Now at 63, after a very variegated career in and out of school and on and off the concert platform as a singer, I've lost my voice but love my piano teaching practice which has everything from promising 4-year-olds to a woman my age who seems to have done at least grade 3 when she was young but who has forgotten ALL of it and is enjoying re-learning; I have late teenagers who are "ticking over" - don't want to work for an exam but want to keep up playing; adults who have just discovered the joys of music and willingly do a theory question each week but often find another week has gone by without practice.
I'll take them all on. The piano is DIFFERENT from any other instrument: if you take oboe lessons it's because you're going to try to perform on the oboe, either in an orchestra or as a soloist, even if you have no professional or even advanced aspirations. Not so the piano. It's what some people use as a doodle pad for their musical expression, or a back-up for their main study, or a place to work out their music theory or the frustrations of the day. It's complete in itself in a way in which few othyer instruments can hope to be. It's a vehicle for learning musicianship. And I take all that on board when accepting a pupil. You'd be surprised how many parents will be prepared to pay the going rate just to keep the interest alive in their kids while they are concentrating on something more academic, with limited time to practice hard.
So - depending on what you expect your piano playing to develop into, I'd say that if you're following plenty of other musical experience, a spell of a few years just playing and exploring for yourself will probably do you no harm at all. When the time comes for you to take the actual performing side of it more seriously, you will feel like taking