There is currently petition citizen initiative underway to urge the European Commission to connect all capitals of the EU with high-speed rail.
I’ve already signed it, are you joining ?
https://europa.eu/citizens-initiative/select-language?destination=/initiatives/details/2023/000004
Edit: It’s not a petition, it’s a citizen initiative.
What about the different railway widths?
Ask Spain… They have both the common gauge (and use it for HSR) and a historical larger gauge. And they have gauge changing trains!
Check out this great video that explains it all: https://www.youtube.com/watch?v=J949O1KQhuk
From what a quick Google search / Wikipedia hunt showed me is that most of the EU (with the exception of Russia and Finland) are already running on “standard-gauge railway” for their high-speed rail
Sources:
https://en.wikipedia.org/wiki/Standard-gauge_railway
https://en.wikipedia.org/wiki/Track_gauge_in_Europe