Several things:
First: Of course there is GM immersion. The GM has to be able to “see” the world in his mind so he can describe it adequately to the players. Immersion is more than just “feeling like you’re there”. Nobody at the table thinks they are an actual high wizard or barbarian or sth. You can tell by how they are saying “I swing my axe” instead of actually swinging an axe. Immersion just means how coherent and complete their mental picture of the world and their characters place in it is (which comes with an empathetic connection with the character). The GM is doing the same thing to a lesser degree for many characters (all NPCs at the least, but also the PCs).
Second: Your workflow diagram is only describing the simplest case of “Straight roll with predefined modifiers” and omits the kind of important part of actually rolling the dice and doing math with them.
Third: You entirely neglect the fact rolling a die is often actually fun. Blowing on it. Pleading with the dice gods to give you a good result. Yelling “NAT 20!” or whispering “NAT 1” in dismay (or whatever your systems equivalent is). Putting a badly performing die in prison. Borrowing the lucky die from another player and negotiating lending fees. Rolling 15d6 to see how much damage your nuclear leveled fire ball actually does.
Ultimately, you should play how you and your table enjoy it. I wouldn’t want to play at a table where some players (the GM is a player too) don’t get to make any rolls or have to make all the rolls. You do you, but to me that sounds like a terrible time.
PS: During the pandemic my table switched to a VTT and I enabled automatic saving throws. I had to disable that feature because my players HATED “the computer” rolling for them. They insisted that they must be the ones to click on the “roll saving throw” button. If I tried to take their rolling during live gaming I would loose the table.




Because in my experience meta gaming like that is not an issue at 90% of all tables. And at the other 10% it’s just that one guy that causes an issue about trying to meta game their character out of consequences.
RPG Rules are not laws, so they are not written for the lowest common denominator, but for a group of well meaning, socially functioning, above room temperature IQ human persons with a base level of trust.
Not every table preference has to be mentioned in the rules to be legitimate. At my table, there are no secret rolls or checks that a PC makes without a reasonably clear concept of what the consequences of success and failure are. So a list of default stats that your GM can check would be a waste of time and book keeping. If your GM likes to use mystical rolls with undefined consequences and the percussion of hidden dice to increase tension, more power to them. But to me that seems a waste of everybodies time.