It’s much less noticeable than said-bookisms, which have been thundered against before.
Of course, leave it to TVTropes to start the page on the subject with one of the amusing examples:
Could it be a factor that many of the western and such books were written at a time when authors were paid strictly ‘per word’? I’ve read that many a western hero never hit the bad guy with the first bullet so there were lots of “Bang! but whitehat missed.” “Bang! Black Bart shot, but also missed?” until 5 or all 6 bullets had been used. I even remember a story of an editor complaining “Is Whitehat ever going to become a better shot?” being answered by “Not at 1/4 cent a word, he’s not.” 
Where the “Said Red, said Ted, said Red, said Ted” convention gets infuriatingly annoying is in audiobooks.
Especially when Red has a western drawl, and Ted a clipped brogue… and the “saids” are inserted in the author’s neutral speaking voice.
I skip all those when I’m reading out loud (to kids, or at a short story party), especially when the speaker is obvious. WHY can’t audiobook narrators do that? I stopped reading one book due to that (plus the reader had the worst Amurr’can accent… the one character from Boston sounded a lot like John Wayne).
I always avoid using “said” when writing dialogue. Not that I replace it with painful thesaurus-fuls of alternatives like “uttered” or “exclaimed” or anything like that (unless they’re appropriate, like a shout or whisper might need). I just frame it with a sentence in a way that makes it obvious who is speaking. Easier to do in a back-and-forth between just two characters.
ETA: I see MrAtoz basically just said the same thing.
As I said (no pun intended), though, I’ve sometimes gotten lost in a back-to-forth dialogue without any speech tags and have had to start all over again to figure out who said what to whom. So I appreciate an occasional use of them.
Zane Grey is strange to read now, but it’s not because of his dialog. His words are actually quite OK. And his descriptions of the desert wouldn’t appear in modern pulp fiction, but they aren’t painful.
Plotting is slow by modern standards, but what’s jarring is his virtue signalling / political correctness, which is – different --. It’s close enough so that you can see what he’s getting at, but also discordant. His strong female characters are… the wrong kind of strong female characters. Dickens doesn’t have that problem: his good characters are good, and his bad characters are bad. Zane Grey has moral ambiguity, and it falls in a strangely dated kind of place.
From the original (1929) version of The Hardy Boys The Secret Of The Caves…
“What a queer duck he is!” exclaimed Biff.
“I’ll say he is!” ejaculated Chet Morton.
This is a good recipe for food to read such books by.