There are a huge number of proofs published every year which assume the Riemann Hypothesis. So while you're technically correct that this only gives us confiden

There are a huge number of proofs published every year which assume the Riemann Hypothesis. So while you're technically correct that this only gives us confidence, it does significantly reduce our uncertainty and compartmentalize it to the Riemann Hypothesis. That's really what assuming the Riemann Hypothesis is useful for in modern mathematics. You can obtain new results for a wide variety of things using the following routine: 1. Assume the Riemann Hypothesis is true and attempt to prove your theorem. 2. Now assume the Riemann Hypothesis is false and attempt to prove the same theorem. If you were only able to prove your theorem under one of those conditions, you have a nice result. If you were able to prove the theorem under one condition and disprove it under the other condition, you've got a great result (see the list of things which are equivalent to Riemann). And of course, you might find that you've proven or disproven the theorem for both conditions, which is still good.