> But if you know that the current company cannot pay like the other company you are interviewing for, or that in this new company the future salary outlook is much better, why bother asking if they can pay you more?

That's situation-dependent: there's often stuff a company can do if you're highly cash-motivated (promotions, other title changes, bonuses, …) to retain you.

On the other hand, often there's not! Especially in older / larger orgs or ones with unconventionally rigid payscales. Even in that situation, I'd generally stand by the recommendation: there's a chance they will find a way to accommodate your needs, and if not you have cemented a strong relationship with your manager and above that will benefit you way into the future.

A few other commenters have mentioned the benefits they have realised by leaving gracefully. IMO this expected upside outweighs the short-term risk, at least in the sorts of roles the post is (now) aimed at.