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Because information theoretic security is a property of a randomness source, not its output data. And it has a stringent definition.

The idea that "I'm throwing the output of some randomness source at Diehard, and if Diehard says it's good then the source provides information theoretically secure random numbers" is a category error at best.

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Could you provide the stringent definition regarding the randomness source, not a cryptosystem?

I see it as this: if the randomness source cannot be one more time put into the same conditions that it would start repeating the same sequence, and its output is random enough (i.e. passes the tests), it may be considered safe for OTP key data production.

The randomness quality is part of OTP's definition, so your "random enough" and "considered safe" places you squarely out of OTP territory, back into "homegrown stream cipher".

Then why are you avoiding providing this definition here?

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