|1: 5e D&D actually has one optional suggestion of the DM rolling everything. Its been suggested as a method as far back as AD&D in Dragon.|
2: The OP was asking about the extreme end of the immersion spectrum and that can get very close to removing the game part or even removing the DM. Depending on how far at the extreme you wanted to get. If its merely "The DM handles everything and the players interact with the mechanics as close to nil as possible." then its still a game.
"The Referee rolls 3d6 for each requisite of the Character"
Note: That the player does not roll their own requisites is very interesting and suggests that the Referee always rolls the dice, never the players. I mean after all, at the point of creating their Character one would think this is the most logical place for the player to roll dice, if there is any place at all.
As to the second point...
When I first started GMing in 1978 I didn't let the players even know my homebrew rules at all. My play mode was completely 'Behind The Screen'. I rolled everything and they role played their characters. I didn't use miniatures, nor did I show them the maps. They had to map on their own from my descriptions of the terrain or dungeon, and quite often they got it wrong, which was part of the fun of the game.
The reason I, and my fellow GMs in my town during this period, chose to write own own homebrew rules and not show the rules to the players was to cut down on rules lawyering, and to allow the players to immerse completely in the world, rather than focus on the mechanics.
No matter how you do it, there's pros and cons, and the more you lean to one side, the more you get the benefits and deficits of that mode.
So now I play a kind of fused-hybrid mode. Sometimes I get down and gritty with maps and tokens, and it's very specifically about tactics of combat. Other times it is fuzzy and narrative. The choice largely depends on the circumstances and how perceive the mood of the room. Sometimes we simply want to romp through the story and tactical considerations, being such as they are, burden us with details that slow the story down. Other times the players seem rather intent on "getting it right" with a specific combat situation, and don't want to take any chances. In these cases they get very detailed with the ranges and positions and order of actions in order to maximize their changes of success.
As for me, I genuinely enjoy both modes, and so I play it either way and it suits me fine.