A lot more direct routes are on the brink of popping up in Europe, EU launched a very ambitious 2035 and 2040 plan.
We've already seen a few routes like Copenhagen - Prague pop up, due to expected new infrastructure (Femern Tunnel) landing soon.
Once EU legitimately builds high speed rails connecting all European capitals, I bet ya we're going to be able to cross the continent with 3 layovers. As long as we stick to larger cities, add 2-3 stops for local connections if you want to go to smaller areas and 2-3 stops if you start in a smaller area.
Sources for the EU high level plan:
https://transport.ec.europa.eu/transport-modes/rail/high-speed-rail-plan_en