Ballots are placed in a pile and opened later, that's the same thing.

Sure someone COULD cheat and look at the vote before its out in the like but that doesn't happen.
In your case what prevents someone from opening the second envelope and then resealing or placing inside a different envelope?

Bottom line is the process we use now is just as anonymous as the one you mentiond if you trust your election chairs (which we do without exception)