I don’t see why this wouldn’t work, in the right context.
The problem I see lies in the way people react to text over images. This is probably going to oversimply things, but here goes. If a character is presented purely in text, then the player’s mind is free to visualise how the player character looks. That’s actually part of the immersion; the player has to create that image of themselves, and if the author is careful it can be pretty much any way the player wants (Gaining Perspective is a good example of this - it leaves some appearance things undefined and if you’ve played it then you’ve probably imagined details that aren’t actually there). It improves immersion in the character. Similarly if you’ve read a book and later seen a movie of the book then it’s likely that the actor won’t match how you imagined the character to be.
Another work around in a text adventure is to allow the player to define how their character looks at the start of the game, then substitute in there choices whenever needed. It can be fiddly to do, but the character will be how the player imagines themselves to be to some extent.
If you are going to have an image of the character displayed then you don’t leave things to the player’s imagination. Have a fixed player character and you run the risk that some players just might not like the one the creator has chosen for them. Offer customisation so they can play who they want and you’ve a lot of images to create and composite on the fly. A middle ground is to have a few choices the player can pick from (and not customise). Any kind of choice adds complexity (gender, skin tones, face shape, eye shape, eye colour…).
A middle ground is the black and white artwork found in comics. Because (on most pages) the isn’t a lot of detail the reader is forced to imagine the rest of the picture, and that makes them engage with the story more. Tainted Elysium did this rather well with just a silhouette of the character showing the body shape, but allowing the player to fill in the details.
Yes, text requires more of the reader to play, but fosters more engagement. Graphical things are easier for the player, and (much) harder for the developer, but run the risk of less identification with the player character.