clarry: I don't think it's a question of technology at all. Games can be immersive enough already.
It's just that game developers (and I guess most gamers) think that games should be about slaying monsters, killing enemies, grinding XP and gathering loot, doing quests, beating bosses.. IMO that just doesn't mesh well at all with deep and meaningful story telling or "tackling serious problems" in a convincing way.
One of the most touching aspect of movies is undeniably in empathy for characters and their interpersonal relationships, but it is very hard to build that kind of thing when it's reduced to snippets of dialogue between hours of slaughtering mobs. It's difficult to build any real sense of urgency without putting the player on a literal timer, but that will 99% of the time just frustrate the player as they want to take their time to explore their surroundings. So there's obvious impedance mismatch between a story trying to make something sound very important and urgent and the player just running around freely in the world doing whatever they want to ... the other alternative is heavy reliance on strong scripted sequences, but that is also not exactly a gamer favorite.
Of course the ones that push the boundaries on storytelling are the devs who abandon these repetitive and mechanical gameplay elements -- but the result is more like an interactive movie or walking sim. Or a VN with no gameplay at all.
I just don't think traditional gameplay is a good fit for good storytelling. But it certainly doesn't help that game devs aren't exactly geniuses when it comes to writing and worldbuilding.
Gosh I really hope GOG releases more VNs soon :\
Technology could aid in providing more means to... scuffle away the mechanical part in games, but yea i understand what you are getting at. Still if a game would be handled in a way such as uhm Saving Private Ryan, I believe medal of honour did go that way once (or one of its other brothers in arms). And the recipient is uhm, let's say old and interested enough to be willing enough to be guided through a series of events that may lead to questions meant to raise awareness of certain horrors that goes beyond a microsecond of attention span aimed at 'discomfort' then i'm sure something could be reached. Has been reached many times.
That said, i also think that with the whole scene taken into account there are many many(like alot) of venues that provide that seriousness the OP is looking for ( :p ). Be it through protest, digging up facts, daily gamer discussions or talks etc....
Personally, as someone who likes to go on adventures, usually dressed up as some fine looking young lady (don't ask) or dabble a bit in rpg's i can't see myself agreeing with the conclusion about how traditional gaming is not a suit fit for stories