So after the umpteenth iteration of "5e effects are mild" and "failing saves is interesting and fun", I decided to take a closer look at what monsters actually do to you.
Aboleth (Challenge 10): Wisdom save or be charmed until the aboleth dies or is on a different plane from the target. Charmed target is under the aboleth's control and can't take reactions. Whenever the charmed target takes damage, they can repeat the saving throw. No more than once every 24 hours, the target can also repeat the saving throw when it is at least more than one mile away from the aboleth.
Hm, so if you fail this save, and the aboleth keeps you nearby, you might never get to save again to regain control of your character. Sure that's both mild and fun. Next!
Banshee (Challenge 4): All other creatures within 30 feet of her that must hear her must make a Constitution saving throw. On a failure, a creature drops to 0 hit points.
Now this one I'll grant is "milder" than a straight up save or die, but an area effect that ignores hit points and can cause a TPK isn't all that fun to me, but to each their own.
Cambion (Challenge 4): One humanoid the cambion can see within 30 feet of it must succeed on a Wisdom saving throw or be magically charmed for one day. The charmed target obeys the cambion's spoken commands. If the target suffers any harm from the cambion or another creature or receives a suicidal command from the cambion, the target can repeat the saving throw.
Not as bad as an Aboleth, since there is a time limit. But losing control of your character for a day, especially from a creature that can disguise itself as a random joe in a crowd, yeah that's "interesting all right. Next!
Carrion Crawler (Challenge 2): The target must succeed on a Constitution saving throw or be poisoned for 1 minute. Until this poison ends the target is paralyzed.
This effect is shared by several monsters. Basically it's Hold Person, except you make the saves at disadvantage. Yep, fun and interesting. Next!
Chuul (Challenge 4): see Carrion Crawler.
Cockatrice (Challenge 1/2): The target must succeed on a Constitution saving throw against being magically petrified. On a failed save the creature begins to turn to stone and is restrained. It must repeat the saving throw at the end of it's next turn. On a failure, the creature is petrified for 24 hours.
Petrification is a lot milder in 5e than most previous editions of the game. And the odds of turning to stone from a Cockatrice is pretty slim- it has to hit you with it's +3 to hit and you have to fail a DC 11 saving throw twice. But still, Challenge 1/2?? So you can face these things right off the bat, they can take you out of the picture for a day (or longer, if there's any enemies about who can do something dastardly to your stone form), you can run into multiple Cockatrices fairly quickly...and long before anyone has any way to deal with it. Next!
Dryad (Challenge 1): basically the same as the Cambion, but Challenge 1. I'd raise an eyebrow more at that, but you're not actually controlled, and Dryads traditionally won't abuse this effect the way I bet a Cambion would.
Spellcasting Enemies: felt the need to comment on these. Most spellcasting monsters can cast spells at a notably higher level than their Challenge (the worst offender I've found to date is the Illusionist from Dead in Thay who can cast Phantasmal Killer as a Challenge 3). A Challenge 7 who can cast 5th level spells? Perfectly fine. Fortunately, despite having access to higher level spell effects, which can get quite nasty, in 5e, it's more about the save DC than the effect- sure that Drow Mage can use Cloudkill, but it's only a DC of 14.
The effectiveness of bad guy spellcasters is highly variable, so it's hard to really comment on how dangerous failing saves against them is- it's highly dependent on their spell loadout, since not all spells are created equally, but spells are pretty much the nastiest things 5e can throw at you.
Even though I only got as far as "E" in the Monster Manual before I stopped caring, lol, the following things seem to be true:
*Nasty and un-fun penalties for failed saves do exist in 5e.
*Very high DC's for saves do exist in 5e.
*It's possible at some point for a player character to encounter a saving throw they cannot possibly make.
*However, the combination of extremely dangerous effects that have extremely high save DC's seems to be rare.
*On the other hand, there are extremely dangerous effects on low Challenge monsters, so it does become quite possible to face a trio of Banshees or a pack of Cockatrices at some point. Even a high saving throw can fail if tested enough.
The bottom line is, while some enemies are problematic in the extreme, I think a DM would have to go out of his way to employ them often, and a canny DM knows what the effect of such monsters can be on his or her game. I think that puts this discussion to rest, once it gets to the point of "a jerk/inexperienced DM could kill their party and suck all the fun out of D&D", because that's a problem with those kinds of DM's, and not the system's fault.
Also, some people LIKE playing D&D when you can die (or worse!) at any given moment. And it's perfectly ok for the system to support that kind of play.
Most of my experience with 5e is with public play, where you have less control over what enemies are used, and the adventure designers are happy to pick some of the more ridiculous enemies at times. In that environment, the intersection of dangerous effects + high DC's is a problem, but again, that's not really the system's fault.
I'd be happier with a game that puts less of a burden on the DM to not accidentally create "impossible" encounters, but that can happen in any system, no matter how well balanced.
Short and Sweet: highly dangerous enemies and stupidly high save DC's are a tool in the DM's arsenal in 5e. How fair and fun this can be is highly subjective to a given group's playstyle. I don't like it, but I fully acknowledge that it's only a problem if the DM makes it one, and you can't take the system to task for how it's tools are used.