As always this is grossly oversimplifying. As well as the misleading safety stats, as graemep has noted, it ignores that journeys just absolutely exploded under privatisation [https://en.wikipedia.org/wiki/Privatisation_of_British_Rail]
https://en.wikipedia.org/wiki/Impact_of_the_privatisation_of...
(I remember being amazed as a kid in the 90s on encountering a mainline train that had automatic doors. Irish Rail was pretty behind the times for a long time.)
Also higher revenue often means better service, which for most people is more important than the price.
https://en.wikipedia.org/wiki/List_of_rail_accidents_in_the_...