I reviewed my mental prep (I really need somewhere to keep this all, I might write it down on paper, honestly) and most of my c3 ideas just simply don't work according to a computer. I might look into the Anti-Marshall rather than learn the Yates, Pilnik, Marshall, and all the Closed Variations. I'll keep the 4. d3 line against the Berlin and just play play very slowly and passively with d3 h3 0-0 a3 Nbd2 Re1 Nf1 Ng3 Be3 Qd2 Ba2 and force Black to fight, something a Berlin player won't want to do.
The Anderssen Variation (5. d3) and the Martinez Variation (6. d3) are quite playable and lead to very similar positions as the 4. d3 Anti-Berlin. Nils Grandelius published a course on Chessable that uses the Martinez as the base of the repertoire (with the Anderssen as an alternative), if you are interested in checking it out (he also uses the 4. d3 Anti-Berlin in that course).
As for the second reason, I'd argue that it's a bit slow, as d2-d3 c2-c3 d3-d4 gives Black an extra tempo compared to c2-c3 d2-d4...
Well, yes... but if you are playing for c2-c3 and then d2-d4 (in one step) then you have to do it (and risk an open center) while half of your army is still on their starting squares... yes? NONE of your QR, QN or QB gets to move while you have Pawns sitting on d2 and c3.
While the alternative I suggest is to play d2-d3, c2-c3 (now the center is kept under control), then get castled, develop your WHOLE army, or at least as much of it as you like (eg: Nb1-d2-f1-g3)... and only when you feel completely ready do you play d3-d4.
A lost tempo on move 12 or move 15, when you are completely developed anyway, is NOT the same thing as a lost tempo on move 5.
I reviewed my mental prep (I really need somewhere to keep this all, I might write it down on paper, honestly) and most of my c3 ideas just simply don't work according to a computer. I might look into the Anti-Marshall rather than learn the Yates, Pilnik, Marshall, and all the Closed Variations. I'll keep the 4. d3 line against the Berlin and just play play very slowly and passively with d3 h3 0-0 a3 Nbd2 Re1 Nf1 Ng3 Be3 Qd2 Ba2 and force Black to fight, something a Berlin player won't want to do.