I agree.

Maybe Gonor and Rohan could have continued doing more or less what they wanted, the threat of imminent death being grossly exagerated

I don't think so. At least Gondor was too close to Mordor to stay safe. An attack on Minas Tirith wouldn't require a lot of supples etc. The same with Pelagrir and that is the two most important cities of Gondor. And with a base there you could launch an attack on the rest of the country.
Rohan is further away, but a part of the deal was that Isengard would be handed over to Sauron, so Rohan would eventually been an unsafe place too.

Meneldur