Hi there! What you're describing is absolutely normal. I don't think they can really understand why they have to stick with you when they're this young. They are just trying to assert their independence and have no clue of the dangers around them.
Like you, I wasn't thrilled with the idea of a leash, but then my 2 1/2 year old got away from his grandma at the zoo. He loves to run and just took off. Thankfully another couple with a small child stopped him and she caught up. But the thought of what could have happened just completely freaked me out! Thinking about it still makes me cry! So, the very next day I reserached the 'leashes' and ordered one. Until he can learn to stay with us, he's either buckled in the stoller or buckled to an adult! I don't really think it harms their psyche or degreades them or anything - they're too young to even know what that means! And to anyone who says it's harmful to them, well - I say they're going to be hurt a lot worse if some sicko grabs them!
Anyway, here's a link to the one I ordered. http://www.opair.net/. I gave it to Caleb as a 'special present' and he loves it! I asked him if he remembered how scared grandma was when he ran too far away, and told him this was to help grandma from being scared. He even wants to wear it in the house and wants us to hook him up - so we won't be scared. He thinks he's protecting us. It's too cute really!
Good luck!