Depends on whether you want to "perpetuate the myth", or disillusion a whole generation, by showing just what a bunch of self important scum bags these people actually were.
The law men were all drunks, most like the Earp's got famous enforcing some form of "No guns in town" ordinance.
After fighting for 40 years to regain the right to concealed carry and self defense, do we really want to glorify the original Brady bunch ?
Then of course there was the whole issue of them being paid based on the fines they collected, that was a very lucrative shake down.
Matt Dillon was a much better role model, do you actually want to show off alcoholic extortionists as "the American Ideal" ?
None of the real ones "rode off into the sunset, they were more likely to stagger back into the bar.
Tom, you are way off base here. Did they drink? Yeah. Were they drunks? Not hardly, they would have been dead if they were drunks.
Tilghman was a Town Marshal in his 70s when he was killed by a drunk Revenue Agent. The agent was drunk, not Tilghman.
Holliday was probably the closest to an alcoholic, but then he was a lunger, so the drinking probably took the edge off the pain of the disease.
Custer was foolhardy and headstrong, not drunk at the Little Big Horn. He was drunk on duty earlier in his career, and went AWOL to see his wife - hardy atypical in the Army in those days. Hell, Sickles killed a man in DC for diddling Sickles' wife, and got promoted - and acquitted. There is no indication that Custer was a drunkard after that earlier episode.
Bass Reeves was damn near a teetotaler IIRC. He was cold, methodical and one of the best man-trackers and Marshals in the west.
History is about the reality, both as a positive role model for their actions, and as warnings against their failings.