Exactly. I pick up my authenticator just after I type my password and hit "enter". By the time it verifies that and pops up the authenticator prompt I am ready. There is little to no inconvenience.

I also bet people will lose authenticators a lot more often if they go months between being prompted for them. The need to enter the code at every login means I am mindful about where my authenticator is (and remember to bring it on trips if I want to play WoW).

less secure? explain please.

depending on how this is implemented ( there are many things that Blizzard could mean by "your computer") There is no less security with the new system. Imagine that Blizzard is using a rigorous hardware ID+IP+MAC+geography type of signature for "your computer" in that case the only way to log onto your account is to:
a. Have the authenticator registered to the account
b. Be in your house, sitting in front of your PC

Do you live in the same neighborhood as a Chinese gold farming operation? ID your home frequently broken into by thugs whit a taste for uncut gems? You are not less secure now unless Blizz totally failed the implementation of this, like using IP only, I am confident they would not take that risk, I would say that the game is MORE secure now because there is one less excuse available to the authenticator haters now.

Ok. So Blizzard is using our 'computer id' to determine if we need to authenticate or not.

So blizzard scans our computer and comes up with the 'computer id' of "387aghd765343&^$". So any time that it's reported to blizzard on login that the computer id is "387aghd765343&^$" it will not ask for the authenticator.

Without knowing what the algorithm or procedure that Blizzard is using to determine that string, I cannot be certain how easy it is for a gold farmer to obtain that information. Is it easy or likely? No. Is it more likely than them cracking the specific time/date algorithm that MY unique authenticator uses? Quite possibly.

Everyone's defense of this has been that a hacker needs to be at MY computer to enter without authentication. The reality is that they only need to make Blizzard BELIEVE they are at my computer, and we have no way of knowing how complicated that will be for a hacker.