On one character of mine I wasn't really specializing in any one thing. I did alchemy and enchanting and smithing. I used magics, mostly restoration and destruction, and I used shields and swords. I guess I did specialize in one-hand though because I didn't like how slow two-handed fighting seemed.
I did take only two perks in smithing and those are Steel Smithing and Arcane Blacksmith. Other than that I haven't taken anything else. As you say, you can find everything else eventually.
Heavy Armor got perks as it leveled too because that was the armor I chose to wear but now I've maxed out that skill, but not all the perks in it, I'm using light armor more since I like the bonus' that I get from the set I'm using. My archery and sneak got leveled up also because I like to try and even the odds first before taking on a mob and I put perks into each of those to help me there.
In general though that character is a jack of all trades.
Now my second character is primarily an archer. So, Archery, sneak, light armor were my primary focus. Smithing again got some attention so I can improve the weapons and echanting got some too so I could make a weapon I wanted until I could find one I liked better. I'll probably not improve that character more with other skills, although restoration and destruction might get some attention so I don't have to carry around all the healing potions and I can us lightning on some of the critters that I need to interrupt their magics. Although, the combined skills of sneak and archery have proven quite affective in dealing with most.
So, to answer your question, lol, nope you're not the only one level all your skills. I like to let my skills naturally progress instead of using the exploits to ramp them up quick.