Based on the way the game is run according to the books. I can't account for every possible subsystem used by DMs in what I'm saying - which is that there is no mandate for hiding this information.
Plus, playing the way you described would cause combats to take longer than they already do, with questionable benefits
Very true. I just am all in favor of things that emulate "fog of war" - which what we call any kind of flub, miscalculation or forgotten action at my table. "Worse things have happened in the heat of battle," we say.
The wizard had cast protection from arrows on two others and there was just some confusion about who got what. What did we do? We didn't take it back. . . We just rolled with it. . . In the frantic preparations for the barbarian attack there was a poor assumption made - it made for drama and a funny confrontation after the battle.
Anyway, I have found that allowing people to count things out before they do them (in my game, if you count out boxes for character movement you have moved that way, no take-backs (on the other hand I do warn players about potential AoOs as they approach them)) leads to slow downs where folks try to figure out the exact perfect way to move and try several possibilities before choosing one.
The player could have missed the spell casting information because he was crunching too loudly on a cheesypoof at the time. That would be one of my qualms about this personally - that the players reason for missing the information would not be applicable to the character's missing of it.
I'd hate to enforce a table rule if everyone but me would be annoyed by it.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.