why dota 2 has more picks than LOL

It has to do with STR AGIL and INT balancing heros much better than simple "+ damage". It helps to balance differences in champion kits, since STR gives literally every stat a tank would want , agil gives balance against all but base damage spells (see why carries build bkbs or linkens) and Int gives casters more spells and damage without giving them HP or armor (once caught, they are done for)

So say if you have a hero who has X skills. These X skills are worth a certain amount of balance points. With dota, they simply need to adjust STR gains, since each point gives a uniform amount across all champions. With LOL, they need to adjust all these different stats individually for each champion, which is why some champions are usually weaker than others.

This is also why items in Dota2 are superior, since the items each give unique values depending on who uses them (so, for example, a carry buying a BKB does not gain an extra 10 damage, since they do no benefit from str). I cant tell you the number of times carrys in LOL buy items orignal designed for tanks throughout its history, but it is a ton (warmogs, sunfires, sterraks, hexdrinker, black cleaver, atmas, heart of gold, leviathon, ) theres probably more as well.