It’s cold in the fall and all the players get are those heated seats.
Man, there are so many people on the sideline of a football game, 50+ players at the pro level, and an appropriate number of staff to support all those people. It would be a long dugout!
Flip it around: why do baseball stadiums have dug-outs? What purpose do they serve?
The same as a trench in a war: protection. Baseballs move much faster than footballs, and are harder, so getting hit by one can cause serious injury.
Likely largely because it’d be a safety hazard. Players run (or are shoved) across the sideline at high speed, and falling into the dugout (or running at speed into a railing or wall protecting the dugout) would be dangerous. You could “fix” that if the dugout was some distance away from the sideline, but (a) many stadiums don’t have a great deal of room between the field sideline and the stands, and (b) the pacing of football is very different from baseball: teams make substitutions of players on the field on every play, and because time is usually of the essence on those changes, players (and coaches) congregate on the sidelines.
ISTM that about the only “benefit” you’d get from a dugout is getting players out of inclement weather, and that’s why NFL sidelines now have heated seats, players have capes they can wear when they’re on the sidelines, etc.
Not always.
It would be really hilarious if the next batter did the Babe Ruth “Calling his shot” bit, but was pointing right at the dugout 
Probably the only thing that could work would be a simple canopy over the sidelines. Any type of baseball-style dugout wouldn’t work for the reasons @kenobi_65 mentions. Rails/fences, steps, etc. would be very impractical.
Players get more than heated seats these days. They have huge heaters on sidelines as well.
They also have heated stands to put your helmet on, so the helmet is warm when you put it back on to return to the field.
They have these big “cape coats” as well.
And then there are hand warmers that warm up more than hands; you can warm up your feet, your backside, whatever.
All of the heaters definitely help in cold-weather games; the other sorts of inclement weather that can make being on the sideline miserable are heat and pouring rain (hello, Miami). Canopies could help with that, at least a bit; in seriously hot weather, teams usually have misters and fans on the sideline, as well.
Yeah, canopies would help immensely for either of those situations.
That’s a funny video and probably a an MLB record. Don’t many dugouts have a low wall as well? Are there any luxury dugouts?
If they existed, I bet the Dodgers would have one. I’d say Yankees, but they are so stodgy as an organization that I wouldn’t count on it.
More often, a padded railing, with a light fencing between the railing and the ground.
Note that that video, with the Angels’ dugout, is from 1992. The Angels’ dugout today isn’t open and unprotected like that, as shown in this picture from 2023.
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I wonder if they named the fence after that batter?
Reminds me of a story my dad told me. He used to do hammer throw in track and field, and when he started, they didn’t have much in the way of safety fencing. Until the day he screwed up a throw and almost hit the coach…
Baseball players are uncouth (foul mouthed, chewing, spitting, crotch scratching…) and best kept out of the public eye whenever possible.