Well, it's simply a question of where to draw the line. If you don't allow it before the 12 hr mark, you make feck-ups more costly - I don't see it as more or less logical, if you will, it's more a question of how strict you want it to be.
The biggest problem, as I see it, is that the way it works now managers are often directly encouraged (by neutrals) to make changes - which is a) not very realistic and b) not very fair on the opponent.
The halftime principle makes it less likely that someone gets away with tactical blunders: Sure, the downside is that an honest Joe who simply realizes that he should tweak things a little bit (an arrow here or there) can't do this straight away - but there are upsides and downsides to everything.
Plus, purely technical changes are obviously allowed - so if you have simply forgotten an arrow or two, this can be arranged.