How is that helpful? You either have a blue representative that already agrees with you, or a corrupt red one that most likely don't really listen to their constituents, or at least not the one that send mail.

Because that is how democracy works. I you don't exercise it will go away. Also there are Republican representatives who are on the record as being against the executive overreach. Getting feedback from their constituents will give them the support to push back. It really does work.

I believe you may have the causality backwards: ignoring constituents is probably not how democracy works, yet that is what we see today, therefore what we see today must not be democratic.

How can they get away with ignoring their constituents? Well: gerrymandering has made it so that representatives can select their constituents (and their opponent's constituents, or lack thereof). They will remain in their post indefinitely, regardless of this carefully-selected minority of constituents wants, so long as they continue to bend the knee and kiss the ring for you-know-who.

If an existing politician already lacks both the moral compunction and a self-interested political survial motivation to say a thing is bad, then a letter from a minority-opinioned constituent of theirs won't change their mind.