Following good scientific practice I propose a Theory/Hypothesis and now ask you to test it.

Initially this is a "thought" experiment but may progress to real testing depending on your thoughts. Back to the initial question first; My question: Is bitcoin mining itself compromising the security of SHA256?

Possible answers:

Yes (maybe qualified by "in some way" ,etc). No (Not at all because...xxx ,Not unless...YYY). Maybe (??).

The hypothesis is this:

SHA256 is extensively used in many applications (including Bitcoin). It would be of great advantage for many persons, organisations and (not least) governments/military/NSA (etc) to be able to "crack" it.

Cryptographic experts have so far failed to crack SHA256 and only a small number of defects (possible collision scenarios) have been declared which although reducing the theoretical security (of a brute force attack) do not compromise SHA256 in practical use.

SHA256 look up tables exist for e.g. dictionary attacks and are very fast to use particularly for shorter passwords (<8 character). To extend the possibility of using look up tables for longer inputs a huge amount of computing power is needed to run many Terra inputs through SHA256.

This power is impractical to set up and run (cost of hardware, manpower, etc) and if it were set up e.g. by NSA using a super-computer it existence would be apparent and therefore usage of SHA256 would decline as it would be assumed that they wouldn't do that unless they thought they would get a result so users of SHA256 would migrate to a more secure system (e.g. SHA3 series). Therefore what NSA (or whoever) need is a "covert" way of "testing/running" SHA256 and gathering the results.

Is bitcoin mining with its daily 4000+ TH/s power, funded and manned entirely by users of the hardware hoping to gain Bitcoins (and hoping they are worth some real $$) really performing a service for the NSA (or someone) and effectively "hiding in plain sight"?

Methods of testing this hypothesis are invited.