You seem to be confounding content with style.
When I see people who shoot a lot of lots of different things, they often seem to have no particular 'style' because they are essentially just pointing at what they see that is interesting at the moment and taking the picture - as it is.
People who go further than that are using their own particular feelings about the situation to be expressed in how they take and edit the picture.
Typically people with such specific ideas develop their own very specific ways of shooting and that often limits the content to that which fits the style.
For example, Chris (Binga) has a very distinct style that probably wouldn't work for landscapes although it might for wildlife. The content is less important than the expression of it.
Sometimes style overwhelms content like much overdone HDR or pointless street photography.
My feeling is that people who shoot 'everything' often shoot nothing specific very, very well.
If that's the case, then what I'm doing is a waste of time. Maybe photography isn't for me. Hmm, something I'll have to think about.
This is basically the same as with sports. Let's say you are doing it for yourself and you like to play a bit of soccer, a bit of basketball, do a bit of swimming, some cycling and then in the evening you play a bit of poker sometimes with friends or pump iron in the gym. What are the chances that you will be as good as a basketball player, or a swimmer or a bodybuilder? Pretty slim, and even that sounds optimistic. Is it a waste of time then? Not at all, it is good for your health, good for your mind, you meet friends, girls are all yours, and doing sports is better than taking drugs. You spend you time really well.
Now, if you have any ambitions to excel, you have to specialise. You need to choose what you like most and what you are best at. You need to see what possibilities are there for you in any sport. Then you need to decide and concentrate on it, devote your time to learn specifics, practice and master your chosen sport or, if we talk about photography, your genre. Great thing about this approach is that you can develop further and have a feeling of really achieving something, and it will boost your self-confidence in other walks of life, even if it is still just a hobby.
By the end of the day it is all about your ambitions, about what you want to achieve and about what you want from your hobby, whether you like the process or the result. Probably it is also down to a character, some people are more perfectionists than others and they usually specialise. Others have more hedonistic approach and they want to bite every cake on the table. For a hobbyist both ways are perfectly OK in my view.
As for this old Jack of all trades vs master of one dilemma, the truth, in my opinion, as always, lies somewhere in between. Doing everything without concentrating on anything is as bad as narrowing you field of interest too much and never trying to broaden your horizons. Where exactly this "in between" lies depends on your sphere of interest. In photography, in my opinion it is somewhere closer to being master of one.
If you are mastering your favourite genre and sometimes venture into other genres to enrich your photographic arsenal, you will be OK.