Judo is about liveness
Judo's success is due to its free-play (randori) training model, where partners practice with each other in a non-prearranged manner with varying levels of resistance up to full force. Judo dominated the contemporary jujutsu because randori was more effective than the prearranged form (kata) exercises that were then common. Judo's selection of competition techniques was originally for techniques that could be trained with full force safely.
Regardless of whether you compete in the official sport competition (shiai) aspect, randori is an essential judo training element. Competition can be useful as an official, organized way of training with partners outside your school/club.
Judo standing/groundwork ratio is instructor dependent
Although I agree with the stereotype that judo ignores groundwork in favor of throwing, this is just a stereotype. My personal experience is that the ratio ranges from 90% standing/10% groundwork to 50% standing/50% groundwork. I argue that it is far easier to find a teacher with a 50%/50% mix than either a Freestyle judo or Kosen judo instructor.
Judo is nominally supposed to train striking
Striking (atemi) is part of judo kata training. The thinking was basically that a complete system needs striking, but striking is too dangerous to practice full force in randori. Tadao Otaki and Donn Draeger described the relation of shiai, randori, and kata over time in Judo Formal Techniques, which is covered in this answer by Philip Klöcking. Sport competition was never intended to be the central element of training.
My opinion is judo's striking training is mostly useless for the following reasons:
- Kata is already secondary within judo training
- Kata attacks are large and telegraphed
- No one spends any time improving these attacks
Even in clubs where kata is practiced frequently, I think the quality of attacks is far below what you would expect from someone trained in striking.
Combining martial arts is non-trivial
Notionally, it makes sense to take a throwing art and a striking art and stick them together to get the best of both worlds. The problem is that martial arts disagree about things like:
- How do you generate force? For example, do you shift your weight forward while striking? Striking-only martial arts can do this without penalty, but this invites throws.
- How much injury risk is acceptable? Getting hit in the head regularly is well determined to put you at risk for brain injury.
- What should the fighting stance look like?
Mixed-martial arts has been successful combining the ground work of Brazilian jiu jitsu with the stand-up elements of Muay Thai and boxing. I argue this is because BJJ basically has no standing game and Muay Thai and boxing officially have no ground game.
Judo has overlap with both ground and standing techniques, so it's more complicated to integrate.
Things judo does not do well
- solo practice
- some elements of body development: flexibility, breathing, and mobility in the spine to improve posture
My personal choice for covering these elements and "physical mastery" is bagua, but I started this after many years of judo.
Just start with something. Learn some, then adjust once you know more.