I think 'sad backstories' have gotten so ubiquitous because a lot of people assume * reasoning * automatically makes a story better.
The existence of magic in a story is okay, but a * magic system * is better. Natural worldbuilding is okay, but * lore * is better.
And in this case, a villain doing bad things is okay, but doing bad things for a justifiable(-ish) reason you can explain to the audience is better. And the easiest way to lend logic to destructive behavior is to have it motivated by sadness or anger. =/
Of course, like other people have said, there are all kinds of valid motivations for villainy; 'hurt people hurt people' isn't the only available option.
And honestly, sometimes a 'backstory' is just none of the audience's business. ¯_(ツ)_/¯ Other things can be more important...like the impact the villains are having on the actual plot, or their character development in the present-day. That's really all a villain needs to be convincing-- to matter to the story, in whatever way serves it best.
I'd say it's not always needed. I tend to write them in if it makes sense as an explanation for who they are as a person, sometimes for sympathy. If their motivations are pretty clear without the backstory, then I don't feel the need to include it. Most of my villains tend to be atrocious human beings, so I don't feel that bad for them 
Me writing Anopheles' /24's backstory:
I personally hate sad back stories on villains. The main thing a villain needs to think is they are not the villain. Hitler didn't think he was a badguy. He thought he was helping germany becoming a superpower of europe again. Genghis Khan was only a badguy to western countries. To his own people, and most of his conquered territories, he was actually pretty chill and people had lots of freedom of movement and commerce. But he was literally the devil to his enemies. Very few people are bad for bad sake. Few if any would-be world conquering people did it for the sake of ruling the world. They are usually much deeper motivations to what they want to do. The best thing you can hear from your audience is for them to say "I don't agree with the actions, but I understand."
Everyone does something for a reason.....sometimes the reason is simply that they are a jerk and want something without caring about how many people they need to harm in the proccess.
Haha gotta love Eggman 
Indeed I've always wondered about the theme parks so it's nice to see his "reason" behind it! I've always had a sense that he truly enjoyed what he put his time and mind into.
A sad backstory is useful if you wish to make a villain who is, to some degree, understandable or even pitiable. Or if you wanted to make their eventual destruction necessary but somehow regrettable.
Not all villains necessarily have a backstory that makes people sympathize with them
Backstories explain how and why the villain becomes a villain in general. There are villains who seem unredeemable morally, and there are others who seem to be like Heinz Doofenshmirtz or Megamind (Megamind doesn't harm people unlike Hal/Titan).
I don´t imagine them as villain and hero, for me it´s just a question of perspective.
The antagonist could also be the protagonist when you tell the story out of their perspective
they don't HAVE to, it really depends on the tone/ genre of the story.
but even without a backstory, they need motivation even if it's just a simple "I like being evil!!
I'm kinda over the whole sympathetic villains because on how it's overdone. My favorite villain of all-time is Dr. Robotnick from the Sonic games.
He looks funny like an egg shaped but threatening as hell... he has a funny side but still have the balls to fight Sonic in almost every stages in the games. He doesn't simply wait at the end of the game... nah, bruh! Robotnick isn't that type of villain, he'll take you out himself if he has to and that to me is more admirable.
I love my villains to be bunch of assholes so that when the hero drives his/her fist in his/her face, you feel so damn satisfied and their defeat would be even more satisfying. The only reason I'd punch a sympathetic villain is how annoying he/she could get.
Shao Kahn from Mortal Kombat is an awesome villain and he backs it up. He insults you and still kicks your ass.
I don’t think a sad backstory is necessary unless you plan to redeem them later. And them going through the step of character development includes confronting their past.
Tho I don’t think that automatically makes them memorable. Most of the memorable villains tend to be ridiculous, campy, and sort of a diva.
I think the most interesting villains are ones who are just corrupted versions of the protagonist. Like Simba and Scar both wanted to be king. Both sing very superficial songs about it.
Technically, could a villain be an inanimate thing? Maybe the closest example is a rampant virus, or AI. Something like that. I mean, the Martian is literally an astronaut versus the conditions of mars, and those conditions really work against him.
Nah. They can just be like "Welp... I'm here. Imma do my thing". Depends on your angle of the story. Villains are just as flexible as the protagonist.
I said it before, but my favorite kinds of villains are just as vulnerable as the main character. Almost as if they could be a side character or part of the main character's crew due to the fact that they're part of the world they live in.
It boils down to preference.