The more distinctly characterized the MC, the better it is for them to have a face, at least for VNs. KNs it doesn't seem as necessary, as they're usually stories narrated by the MC themselves.
On that note, how about nameable protagonists? If a main character has a distinct personality and appearance, does it mess too much with immersion to be able to name them, possibly after yourself?
EVEN IF THE TENDONS OF MY THUMBS TEAR INTO NOTHINGNESS, EVEN IF I GO NEARSIGHTED FROM STARING TOO HARD AT THE SCREEN, EVEN IF MY BODY IS CLOSE TO COLLAPSE FROM THE 72 HOURS I HAVE GONE WITHOUT FOOD! I WILL DEFEAT YOU!
I've usually thought the "enter your own name" bit was kinda dumb, except in games where you're able to create vastly different characters on different playthroughs.
I think in the VN/story where MC personality is very strong or crucial to the story, MC should have face (or even appear on screen). If not, then he should be faceless since it would add to the immersion (of course it's even better if you could change the MC appearance... but it's not as easy to program).
XChange Alternative Yin-Yang even have the MC sprite shows up just like any other character's sprite.
"Double the princesses, quadruple the fun!" - Haken Browning (SRW-OG Endless Frontier)
I agree with Papillon, inputting a name often irks me particularly if the VN is based on 'their' story and the only thing I alter is paths they take. It feels like I'm giving them a false identity (if that makes sense xD)
Like with many of the older final fantasy games where you could name the protagonist who are referred to their default name anyway.
If it's a stat+appearance customisation game, then I'm all for creating a unique character with a unique name. But when appearance and story are set in stone, it's a bit of a turn off.
In regards to MC's appearing on-screen, I'm used to the old school VN's where you don't see an MC sprite and merely only see them in CG's. I guess my only qualm is in games where the MC appears in a CG but with their face as a blank or their hair covering their eyes. I mean, if you're gonna' show the MC, might as well present them fully :3
All in all, sprite or no sprite, I don't mind either way. I just feel that by not seeing the MC's emotions during the dialogue, you can visualise the MC having the current emotion you're feeling.
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