Capacity is the big benefit. Rail passenger numbers have gone up and up without any matching capacity increase in the train system.
HS2 would put high-speed trains on the their own track, which then frees up space on the existing lines.
This means that smaller stations benefit, because there’d be more capacity for more trains to actually stop and to serve other local/regional stations
It means environmental benefits by getting more people and more freight onto the rail lines and off the roads.
It means more reliable services because of fewer congested bottlenecks
It means we COULD, potentially, reopen more closed lines (like the Borders railway), which at the moment we can’t even if everyone wanted to because there’s not enough capacity on the lines that those closed lines join.
The alternative to HS2 would be upgrading three existing lines - more track, extend stations, rebuild junctions and so on, all the way up. This would be more expensive (yes even more expensive than HS2), more disruptive, and more environmentally destructive because you can’t plan the line route like we can with HS2.
I was against HS2 when I thought it was just about getting to London faster but the capacity argument has definitely won me over.