This works, so long as the players want it to work.
Session 0 is going to be crucial here.
Combat is only one part of the game. To some people, it's an important part. And to some of THOSE people, they want it to be an important part that they have a unique skillset.
If the group is invested in their characters being different, then their character sheets don't matter as much.
Compare how different Legolas, Gimli, and Aragorn are, despite likely just being 3 fighters.
If Mechanical differences are important to the players, then they have to coordinate the characters to reflect that
If the 3 players need their 3 charismatic characters to be different, then they need to figure that out. Deception, Persuasion, and Intimidation (and Performance, I guess) are the Charisma skills and each imply a very different way to interact with the social world the characters find themselves in; think Good Cop / Bad Cop / Weird Cop or something.
As I mentioned, in addition to other skills and backgrounds. A Street Urchin with Deception and Sleight of Hand implies a very different character than a Sage with Persuasion and Arcana or an Outlander with Survival and Intimidation.
Assuming all of that, then the only thing left is for you to work it in. Make notes in your book/DM board/notes app/etc to cater to each specialty. You don't have to perfectly hit each thing every encounter. And combat might be tricky; you might have to have them befriend a local shopkeeper that gives them discount potions for helping him rekindle his lost romance, or whatever. I don't have their stat sheets, so I'll leave combat balance as an exercise for the DM.
I'm currently DMing a game with 4 fighter-healers and it's fine. They have different mannerisms and play to those.
- One is more academically religious, he'll go searching the local churches for clues and contacts
- One is more fanatical for their deity, she'll try to use their guild and church contacts to get more information and talk about her deity
- One is more 'fell into it', she'll use the library and try to sweet talk villagers
- One leans more heavily into their combat side, but he'll still beat on doors and demand answers
I'll admit this is a little more diverse than your saying, but each of them would handle the prompt "You've found out about a derelict demon temple" in a different way (samples listed above), despite all opposing it for various religious reasons.
Years ago, I ran with all martial characters and even they managed to make their characters sufficiently different (think again to the example of Gimli, Aragorn, and Legolas). It wasn't their combat acumen that set them apart, but rather what they did outside of combat. And beyond even their mechanics (stealth, intimidation, knowledge, etc), it was their personalities, the life given to them by the players.
Personality; that's what sets characters in the world, not their dice rolls. A player that only rolls dice to play the game doesn't have a character in the world, they just have a character sheet at the table.
It's your job to give them prompts and a world to interact with, it's their job integrate those characters into the world with each other.
It's everyone's (players and DM) job to work together to create an enjoyable experience