Can I say "I got it" instead in this scene? How is it different?
The meaning of "you got it" here is a way of saying I will do what you asked or provide what you want. It is similar to sure or no problem as Joey is agreeing to Chandler's suggestion. Because of that context "I got it" would not work in the same way. Ex: A: Tom, would you please go bring the cattle in from the field? B: You got it, boss. Ex: A: Hi there. Could I get a cheeseburger with fries, please? B: You got it. Anything else?