Nothing is wrong with competing. And if you are going to compete, you might as well compete to win. There's nothing wrong with that pumping up your ego - especially if its a new experience for you.
I got into martial arts b/c I wanted to become a stronger more confident person both mentally and physically. At 5' 7½", I trained myself from 134pounds to 155pounds, learned how to fight, gained self discipline, and most importantly, found the mental strength and fortitude to face my fears. My instructor was eager to push his students toward competition and I grew to enjoy competition. As bad as this sounds, I also started to build my ego on defeating others. At first it was proving to myself I could defeat bigger stronger guys I would have been intimidated by before. I definitely had a small guy complex, having something to prove.
I don't know if its right, wrong or otherwise. Its what works for me, along with teaching. Some would say its a cop out because I don't have whatever it takes to drive myself to win in competition. Maybe that's right. Maybe its not. I just go to the gym, train hard and try to fix any shortcomings I find in my performance.
I think your attitude towards MA, putting the focus on training, bettering and challenging yourself instead of comparing or competing with others is right. I will adopt this attitude towards MA and training.