I'd say Majikoi's not the best example. There are many faceless protagonists out there, but Yamato ain't one of them.
Not only is his face clearly shown right during one of the initial CGs, his face appears in every non-sexual, non-kiss CG where he is present.
Sure, that amounts to about 6 of them, but it's still a very rare thing.
However, I understand what you mean with Yuuji. In his game, they did not remove his facial features in any CGs he was present (and his long-ish hair is also distinctive on its own) and had plenty of chibi's featuring him, which is quite something. Still a considerable number of purposefully concealing angles, but his face was there, for the most part.
Indeed, protagonists that are their own, with their own personality, and their own voice are typically some of the best in my opinion. Yuuji's got a strong personality and dead fish face image. Shirou from Fate/stay night has a strong personality (and voice, depending on your version) and you saw him right at the start. Rintaro Okabe has one fantastic voice, personality and distinctive labcoat (and a face, I guess). Even Takeru from Muv-Luv was given a face. Ever17 pulled some funny business on that topic. You know everyone's face and voice in Katahane (and with a face like that, I can see why Cero's voiced by a woman). The protagonists in Overdrive titles are generally given distinctive characteristics. Christ, the protagonist from Edelweiss is distinctive because he overuses tie pins -- yet we never actually see his face. Bunny Black has a pretty distinctive looking protagonist, and he ain't a good guy. Comyu's Akihito... Symphonic Rain's Chris... I still remember Tsukihime's protagonist and his oversized, distinctive glasses. Ikikoi, of all things, had a face and personality (whenever he went by un-abused long enough to show it).
The list goes on and on... But for every one of these titles, there's three or four with faceless or not present in CG's protagonists. Which reduces their presence and personality...
It's not impossible to give them some defining characteristics, of course. Edelweiss had his tie pins, Da Capo I's Jun'ichi had his apathetic "what a bother" approach to life, A Profile had ridiculously naive (or optimistic?) beliefs. Heck, Wanko to Kuraso's seemed to be some sort of superman who had any and all skills and could make any woman fall at his feet -- he wasn't even much of a good person at the start of the game.
But if you ask me about Hoshizora's... Or Yuuki from Koichoco...
Pretty much just some generic protagonist I can't recall.
Something, something about them so you can make an image to work off is extremely important. Otherwise you can't even recall them. Even when you forget their names you can still remember them then.
KoiRizo's is distinctly stingy and petty on some matters, but when the routes go and melt that off he just meshes into yet another generic faceless protagonist.
Goddammit, he even has glasses. Why don't they show him?!