The problem is that peak fares can rise to astronomical levels if they are unregulated (i.e. can be freely set by the train operator).
An example: a 2 hour train journey from London to Manchester (approx 200 miles/321 km) one-way booked for a peak-time slot a week in advance can cost as much as £166 (approx €217 / $235), which is frankly ludicrous.
[1] http://www.theguardian.com/money/2016/jan/04/action-for-rail...