Most mathematicians believe RH is true, and generally when doing industrial number theory people operate under the assumption that RH is indeed true and so if they need to use X to justify something and there is a theorem of the form "if RH is true then X" they use X.

Thus a proof of RH is not a problem. It just confirms that what people applying number theory already assumed was correct.

A disproof means that those X's might not be true and their use would need to be reassessed.