The rules forbid using a reaction for spell casting (that includes readying an action, because it uses your reaction too) if a spell with spell slot was already cast as action. So what your player wants to do in your example was in no way permissioned by the rules.
Yes I know, but in this case he did not use a spell slot for either spell.
The only real restriction is you must concentrate from the time you ready to the time you cast. So he could not have done this in reverse - Wall of Fire then Fireball as a Reaction, because he would have had to drop concentration on Wall of Fire to ready Fireball.
The short RAI is: A player can never cast two leveled spells per round.
No RAI is pretty clearly it only restricts spells that use a spell slot (and there are additional restrictions on Quicken spell, but that is not relevant here).
I think JC even mentioned this when talking about the new Fey Warlock and how he can cast Misty Step repeatedly and then cast another spell.