Have to agree with bel_13 here. There are only so many hours in the day, and only so many days in a lifetime. Prioritise what is important to you and don't worry so much about the rest. For example, for someone who wants to be a classical concert pianist, music theory is going to be far less important than for someone who wants to be a jazz pianist. Even there, jazz theory and classical theory are quite different. Sight reading is also almost certainly more important for a session musician than for a composer.Hope that helps.
I have to disagree with this. You can tell when a classical pianist doesn't understand their theory well becasue it will reflect (poorly) in their playing. Or to say it the other way around - a pianist who really understands their theory will have many more interpretative tools at their disposal and will likely play better for it.
I would categorize musicianship skills into two main groups: foundation musicianship skills and advanced / specialty musicianship skills. The foundation musicianship skills are those that all musicians, regardless of instrument or genre can benefit from. Specialty musicianship skills are those that are specific to one's musical interests, and would further enhance one's ability in a chosen area of study. For example, it is not high on the priority list for every musician to be able to give a theoretical analysis on a Bach fugue. Contrast this to, it is extremely important for every musician to be able to sing a simple melody, or perform rhythmic dictation / clapback from an auditory source. First focus your attention on obtaining the foundation musicianship skills. When those skills are secured, then you can consider working on the specialty musicianship skills. A basic list of fundamental skills may include (but not limited to):Improvisation - most of the following should be practised using improvisation.Singing - simple melodies, sight singing without aid of an instrument.Keyboard - pianists generally have this covered, simple melodies, scales, chords.Rhythm - ability to sight read rhythms and solve rhythmic puzzles such as polyrhythms.Rhythmic clap back - ability to imitate a rhythm from an auditory source.Rhythmic transcription - ability to notate rhythm from an auditory source.Melodic sing back / play back - ability to imitate a melody by singing and playing on keyboard.Melodic transcription - ability to notate a melody from an auditory source.Two part singing - simple melodies as duos with another musician, without aid of instrument.Ensemble singing - simple SATB pieces, managing your own part, ensemble cohesion.Notice how there was not much theory in the above list. The above basic skills are needed before getting too deep into theory. These skills will be used to practice your knowledge of theoretical concepts. When one is established with the above skills these can be added:Diatonic scales - all major and minorModes - those based on the white keys of the pianoTransposition - take the melodic portions of the list above, and transpose.Modal change - transpose from one mode to another. Eg. C major to C minor, F dorian to F mixolydian, G minor to G phrygian.