The anime is usually aimed towards the kids, no? Legendaries are usually the best Pokemon in their eyes. The ones the kids are after. I remember my young cousin running around the house with joy and screaming "I CAUGHT DIALGA!" when he obviously caught Dialga, just because it was legendary. Never mind the fact that he was never going to use it anyway, and never mind the fact that he stopped playing the game right after he got it! He still wanted it.
However, with most people on here, you will see Dialga very unwanted and never used in competitive battling or anything, except by people who admire the fact that's it's legendary.
The writers want to show off their beautiful creations, and bring more fans into Pokemon. ;\ That's all. ASH just happens to encounter them because he's the main character. Why can't Richie find one on his own? Or Gary, even?
As for Ash not catching them... why WOULD writers want him to catch them? He would win every battle. Every gym episode would be the same. The season would be over within ten episodes. Even more Team Rocket morons would be after him. Other Pokemon will never be seen again, except Pikachu because he's always out.