Like most mechanics, it can be quite useful and provide several pacing, thematic, and strategic benefits to a game design. Also like most mechanics, the problem tends to be that inexperienced designers assume it provides these benefits automatically, which is not the case.
Just putting "durability" mechanics into a game in a vacuum, without considering how it influences the rest of the game design, is what creates significant problems. This is usually done out of a misguided desire for "realism", which tends to be the sort of thing that inexperienced designers put too much faith in, in general. (Veteran designers tend to realize that "verisimilitude" is actually the thing they want.)
Let's take MGSV, for example. You do have weapon durability--your silencer/suppressor degrades--but it isn't universal. If you wanted to be "realistc", it should be; most firearms do suffer significant loss of reliability if they aren't cleaned relatively thoroughly after heavy use, especially if they're given time to "cool" between uses. There wouldn't be much gameplay benefit to that, though; you already have the ammunition and resupply system there, weapon durability would just be one extra fiddly little bit on top of it annoying the player.
So, why do suppressors get limited shots? Because the designers identified that players of MGS games had often come to equate "stealth" with "just shoot everyone, but do it with a silenced weapon". The AI tech still isn't quite advanced enough to deal with this in a realistic way ("Hey Yuri, have you noticed none of the other guards seem to be patrolling anymore and no one's talking on the radios?"), so the suppressor durability is kind of a stop-gap solution: it's meant to make you consider whether or not it's worth KOing every guard, and hopefully sometimes bait you into leaving a few awake and trying to sneak around them instead, because you're too deeply infiltrated to want to resupply.