I'll need to do more exploration on this topic, but in summary it seems that playing a board game puts your mind into a mathematical and logical thinking state, that prevent immersion to be possible and reduce the level of fun. The only time where fun seems to be added to the game is when the players enhance the game with social relations.
What lead me to that hypothesis is by doing a solotest of games and mechanics. First, I tested a new combat mechanic for a solo game in development. I cannot say the experience was any how fun. Yes it was testing so the mechanics could have been broken. But if I compare to a java demo I made for leading libgdx, the experience was completely different. The demo is an incomplete game that has only 1 level where the goal of the game is to "collect coins and avoid spike". There is not much to this demo, but for some reason, when testing modifications to the code, I could not prevent myself from completing the whole stage even if it was pointless to do. The reason why is because it was fun even if incomplete.
I played elder sign lately solo. While I was plastifying the game, I read the flavor text on some of the cards and got really intriged and scared while doing so. It convinced me to buy some lovecraft books, since I had not read anything about it yet. Then while playing my solo game, I tried doing the same while playing. For example read the flavor text when going for an objective, but I got no experience at all. So maybe while playing the game, needing a mathematical and logical mind set seems to make thematic immersion impossible.
On the other hand probably as a video game it could have been different because most mechanical aspects of the game are not resolved by the players and sometimes they are even hidden to the player which makes the player focus more on the experience and immersion of the game. Elder sign video game might not be a good comparison because the dice play require a good load of mathematics and logic to resolve, but maybe the combat mecahnics I tested above would have been more fun to test as a video game even if the mechanics were exactly the same.
So it seems that the main interest of board game is to have that added value from player interaction to reduce the impact of the mechanical resolution of the game and add fun. It might not always make the game more immersive, but offers an alternate kind of fun.
I was exploring solitaire game lately. So I guess that to increase immersion level, I would still need to keep the game simple, else with too much management, it could reduce immersion.
I'll continue exploring with some solo variants I have in mind.