I expect next gen system only multiplatform titles in the first year of the system launches, and multiple big next gen only titles by year two. Same as past gens.
Big yearly sports games and CoD will be cross-gen until at least Holidays 2022 (probably even beyond for sports games). As usual, JP publishers will have a long cross-gen period (and the Switch even adds to their inertia), Capcom could be the quickest to transition tho.
Then you have big AAA Western 3rd parties and yeah I am expecting a new next gen AC by 2022. New licenses too but still big cross-gen releases like Diablo IV for example (which is only confirmed for PS4/XB1 for now), Overwatch 2, the new Rocksteady game, maybe a LotR game too.
Problem is that most of these big publishers have a reduced output compared to previous generations. Acti has CoD and Crash/Spyro, meaning that they'll stay cross-gen for at least 2 years. WB had a lot of canned projects this gen and it is still uncertain whether their games in developpement will ditch PS4/XB1. Bethesda's Starfield or ES6 won't be ready before Holiday 2022. Ubi has an Avatar game and BGE2 which could be their first big next gen games with AC. Tons of things are changing there currently, which might delay unrevealed games...
My vision is basically this :
Holiday 2020 : big majority of cross-gen titles, a few exclusives at launch like Godfall
Holiday 2021 : majority of cross-gen titles, several next gen exclusives (like AC)
Holiday 2022 : majority of next gen only titles, several cross-gen games (like sports games and CoD).
Talking about AAA games here.