I don't see anything wrong with New World starts - have had many games there. Just finished a game as Aztecs and being able to have colonial nations as your slaves is so wrong.
You don't feel spending 1/3 of the timeline doing nothing is a design problem? That's a strange position to take, but I guess if you enjoy waiting...I usually get enough of that when standing in lines.
Edit: If you feel that 1/3 estimate is exaggerated, go ahead and demonstrate the math of how a 1480 reformed Aztec isn't waiting for 1/3 the period, assuming European border by 1580 and relevant catch-up period after.
If you attempt that math, you'll have a lot of trouble refuting the claim.