I was getting an off-peak train from near London into central London. The train is often packed, with people left standing, and I can only imagine it's even busier at peak times.

Many train lines are at or near maximum capacity and need more investment, if you believe the claims used to justify regular above-inflation rail fare increases.

If economies of scale make them profitable, they should be making money hand over fist.

I'm not convinced economies of scale are the problem.

But those packed routes have to subsidize lower volume routes where off-peak cars will be nearly empty.