This was actually broken in practice once, by (you guessed it) NSA. They managed to break into part of Soviet VENONA since the demand of OTP keymat during WWII

This was actually broken in practice once, by (you guessed it) NSA. They managed to break into part of Soviet VENONA since the demand of OTP keymat during WWII was such that someone took a shortcut and reprinted pages of random numbers. Don't ask me how Cold War-era NSA discovered that without Cray supercomputers everywhere, but even this scheme is difficult to pull off in practice.