Which is not what blinding is. Blinding is not really about adding a random delay as much as it is about preventing an attacker from controlling inputs to variable-time functions.
Also, it's not clear how blinding could be applied to AES.
Yes, okay, however my point was we don't actually need constant-time operation if the timing is uniformly random. Clearly that doesn't mean we introduce a random sleep, but it means we carry out computations in a way that timings aren't data-dependent and an attacker can't separate signal from noise.
Also, it's not clear how blinding could be applied to AES.