After a trip to Paris recently, it occured to me that it would be a
good idea for the tube to offer cheap single tickets in Zone 1, along
the lines of the Paris system (maybe £1 for a single in Z1, £7 for
10).

I think the lost revenue to LU would be minimal. Are there many
Londoners who buy single Z1 tickets? I doubt it - most would have a
travelcard (one day, weekly, monthly or yearly).

The key for tourists is that it would successfully create the
impression of a cheap transport system. If you look at the prices for
the cheapest zone ticket comparing the two systems, you can see what I
mean (all in Euros) - Day Travelcard / Single / Carnet Single:

Paris 5.30 / 1.40 / 1.05
London 6.45 / 3 / 2.25

The difference with the travelcard is not that great (just over 20%),
but the singles are more than double.

The vast majority of visitors would still opt for a travelcard -
perhaps a Z1 card could be offered at about £3.50, which would be in
line with the Paris system?

Not much lost revenue for an awful lot of goodwill and improved
preception of London.