You could do that, but then you have players who don't really know what their Traits do. My preferred method is to sit down with each player with GCS open and go through step by step: Basic Attributes, Advantages central to their character concept, Skills central to their character concept, then fill in some extras until they run out of points. I'm comfortable enough with the major options to walk them through it pretty quickly, although unless someone has a very clear idea of what they want to play, that can still take well over half an hour.

Choosing everything forces the player to at least be aware of what abilities they have. With templates, they still need to familiarize themselves with the included Traits, and then inevitably fiddle with things a bit to get closer to their vision. Accounting for that, I don't think they have much time unless you're playing a very generic character and rely on the GM to keep track of your abilities.