I know what you are wanting and also like some games with compassionate LIs, but bro, the whole plot of NHK was that Misaki was a pretty selfish enabler and Satou only found 'true happiness' when she leaves and he had to pull his weight by himself.
I think some tags at VNDB can help, gonna check them.
Edit: While i search i remebered, i think 'In distant shores' maybe could be what you are seeking. 'The friendship club' isn't perfeclty this but it's a personal recomendation, mainly because of Bella hehe.
Edit: Pretty hard, they don't have a sad or depressed protagonist tag for whatever reason, maybe these could help.
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tag:
This type of a story is designed to have an emotional impact on the player and make itself memorable, crying is usual but mostly optional.
It's explained in
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like this:
The developers at Tactics created a simple formula for a game: a comedic first half with a heart-warming romantic middle followed by a tragic separation and finally an emotional reunion formed what is known as a "crying game". The main purpose of such a game is to make the player feel for the characters and make them cry due to emotional scenarios which serves to leave a bigger impact on the player after the game is over.
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One of the heroines is deredere - she is utterly lovestruck with the protagonist essentially from the moment she meets him.
Expect lots of blushing at even the most innocent remarks.
Combining Deredere with Nakige (deredere with Psycho problems wasn't good) we get some results, but mainly famous JPVNs like Clannad, Air, Da capo and Ef.
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