There is a character in every story. Special One. It becomes the center of the story. i.e. the Main character.

The author takes special care of them. Provides them wise thinking. Good luck. A charm. In some cases special powers, too. Sometimes readers bind that character to themselves, that's how they keep engaging with the story.

I'm wondering, will readers accept a story that has no special one?

How can the story evolve without them? Moreover, is it always necessary to have such a Main character for a story?

Adding to linksassin's good answer about having a cast of characters rather than a main, I want to point out what you said:

The author takes special care of them. Provides them wise thinking. Good luck. A charm. In some cases special powers too. Sometimes readers bind that character to themselves, that's how they keep engaging with the story.

This is an incorrect assumption. It's true that the MC in a lot of genres (I'm thinking about Young-adult fiction and fantasy, mainly) is often special in a way or another, but it doesn't have to be the case. It changes depending on the genre.
This kind of stereotypical Main Character, who wins his struggles because he's special, is completely unnecessary. Fiction is full of protagonist that, while they do have skills and perks, are not "special" nor covered by plot armor.

The real difference between a main character and a secondary one is time; how much time the author spend to show his struggles, describing his emotions and his thoughs, how much time is taken to develop his arc and so on. The more you write about a character, the more the audience will know him/her, and the more they will care (hopefully).

If you don't want one MC, the easiest thing is to have two. Balancing two (interesting) characters, giving each one the same depht and an equally strong story arc, is surely challenging, but it can lead to interesting results. Also, chances are that the readers that won't be able to "click" with one of your MCs will be able to relate with the other. A classic example of this is The Betrothed by A.Manzoni, where both Renzo and Lucia are equally developed main characters.

If you want you can add even more characters and move towards a group cast of main characters. GoT is a good example, but there are many more in literature. Remember that a group cast tend to subtract emphasys from the struggles of a single person to underline the struggles of a group of people, of a political situation, of a nation and so on depeding on the book.

I think you misunderstand the MC; the MC doesn't have to be extraordinary in any particular sense; and in most good stories the MC has weaknesses or flaws to overcome.

The reason an MC is the main character is only because that is the character the reader most identifies with. That is the character whose thoughts and feelings and troubles are shown. They don't have to be special.

Even when they are special, the stories tend to be about problems they can't necessarily solve with their special powers -- Superman's biggest problem (the traditional Superman) was that he is lovesick for Lois Lane, and can't be with her, and can't have a romantic relationship with her. All his super powers can't fix that problem. (In more modern tellings, Superman may hook up with Lois, but again it can't last as a permanent relationship.)

As others have noted, you can bypass the problem a bit using a Main Crew instead of a Main Character, or use a series of leads like GoT, but then they still tend to have a Main Character whose arc we are following for awhile, a fan favorite.

The main rule of writing is the writing must be interesting. We identify with characters doing interesting things. Both IRL and in fiction, we like hearing about extraordinary people, we like hearing about brave people fighting for what is right, defeating evil and cruelty.

So you are going to have to give your character some problem to solve. They don't have to be extraordinary; but also don't make them extraordinarily stupid or gullible or clumsy or foolhardy. They don't have to be a genius, but being so dumb the reader knows they are being dumb is going to be difficult for the reader to relate to emotionally; unless you are writing a farcical comedy (e.g. Dumb and Dumber). In the case of Flowers for Algernon, the character begins mentally disabled; but we relate because he becomes special, and the end is a tragic return to disability.

But these are special cases, you can write an engaging character that is not special in any sense, other than having a problem they feel compelled to solve. Without the latter, you just don't have what most of us consider a "story".

It is harder to keep the reader engaged without one

As you say a main character is someone for the reader to connect with. Ideally they will empathise with them and come to care about the character. Wanting to know what happens to them is enough to keep the pages turning.

If you choose to go without a main character this can be harder to obtain. Instead you will need to draw from a cast of character, each having to work to connect with the reader. For a cast of 6 that can easily be 6 times as much work, plus additional work to manage the transitions. Even more work in preventing readers from disconnecting from the characters you haven't talked about in a while. Writing a good story that doesn't have a main character or characters is hard.

That doesn't mean it can't be done.

Game of Thrones is the most prominent example but there are many others. In GoT the 'main' characters are constantly rotating and we are unsure of who it is meant to be. The main character is whoever the POV is at a given time, each character is treated as equally important.

Calling it the "main character" is just an easy way to communicate the underlying mechanic in its most common form; the main character is just another way of saying, the focal-point of the story, or the thing that catches the reader's interest; what they follow.

It could be a person, a place, a concept, a timeline, and any number of other interesting things. It just happens to usually be a person, because people are interesting and its easier to talk about them than many other things for any length of time in an engaging way.

For example, think of when you were very young and learned a mind-expanding concept in an early science class that captivated you. In an analogous sense, that thing you learned about was the main character of that "story".