It's kind of pathetic that this is the reason Anderson is responsible for it, instead of being a genuine and intentional character flaw. I don't know. It's nitpicky, but I just wonder if they were really intending to make him step down without it being necessitated by the book—not everyone who complains is on the brink of quitting.
There's unfortunately no way to know. In theory you could still have the opening of 3 play out the same with or without the presence of Anderson on Earth. Maybe the resistance does a worse job at holding out if Anderson is absent which'd factor into your EMS score (Maybe the minimum is higher so you'd need to make up for the shortfall so the ground forces coming in from orbit need a larger fleet to get Hammer into London.) Anderson staying behind on Earth is a dramatic beat in the plot that you'd either need to replace with a nobody (so it won't hit as hard) or just outright skip if Anderson isn't present. And for a companion in the opening, you could just give the player Vega.
His largest impact on the plot would be the Cerberus invasion of the Citadel since Udina is the one who opens the back door for them in-game. But annoyingly, you could
still have the same events happen since Udina would presumably have privileges afforded to him by his position + the other myriad insiders Cerberus already have on the station (To memory, you have the Volus ambassador who Zaeed saves and the C-sec officer who gets executed by Cerberus because he stops being useful). Udina is killed trying to open the door for Cerberus which you could still have occur, and his motives (couping the council) can also remain the same. Either Shepard, Virmire survivor, or Anderson himself can be the one to do the finishing blow. And then
after this, maybe Anderson gets tired with doing nothing on the citadel and starts co-ordinating with the fleets like Hackett since he no longer has to play diplomat to get the Salarian and Asari fleets because the player gets them at that point regardless.
The only real purpose of Anderson in the plot is to remind the player how bad things are on Earth, which isn't a bad purpose, but Hackett can also fulfil the same role. His role can be 1:1 as it is in-game after arriving on Earth.
If devs had their hands forced by the book then Karpyshyn is to blame, which'd honestly make me seethe if I was working on the game and now had to orient the plot around the novels of a guy who couldn't get to the end of the 2nd game's development whilst also leaving the conclusion of the trilogy unfinished. Whilst the ending of 3 is by far its worst writing foible, everything else can be lain at Karpyshyn's feet with regards to neutered plot points (Dark energy plot), Cerberus' power spike, Kai Leng, etcetera.