...is probably the sort of thing being thought of.Double all fares.
The thing is - increasing all £1.50 fares to £2 - buses and underground outside zone 1 - would be a one-off unpopular measure but only because we currently consider these things as percentage increases when they happen in January. But loads of stuff in everyday life outside transport use increases like that - in supermarkets, the price of things changes by 50p and no-one really notices because prices go up and down with seasonal availability, promotions etc.The obvious fare oddities to get rid of are the Euston - DC line stops and Liverpool Street - Cheshunt peak 'London Terminals' legacy discounts vs Z1 fares (most of the order of 20 or 30 pence, the biggest being 70p).
Brentwood needs rezoning, or Amersham and Chesham become zone 8 (single fares are only 10p cheaper, with a couple of minor exceptions. Though peak time caps/seasons are quite a bit cheaper from Z8) - they have very different fares. Then all that needs changing on the TfL scales to make them just one is the off-peak fares not involving zone 1. Or just keep them different scales - you might as well use different scales outside zone 6 (or 7 or 8) which are controlled by the fare-setting TOC. And then the contactless-only and "Merstham and Horley are in the same zone" nonsense could go.
I believe the flat fares within Z2-6 (and the similar fares from Z7-9) are revenue generating, getting marginal passengers onto trains, so I'd reduce the Anglia fares to those (one would be a 10p raise, but most a reduction), rather than the other way around. You want (except for under the specific unusual circumstances we have at the moment) to encourage outer borough off-peak users onto the tube, even if they are travelling greater distances as inner-London journeys but paying the same fare - you are running the trains, and the marginal cost is little, so the more the merrier!
Gradually reduce the premiums for South London by increasing NR fares slower than TfL, and NR+tube fares even slower, if at all.
£2 is possibly what the bus fare would have been anyway from January 2021 without the freeze.
Is the demand that elastic outside Zone 2-6 that charging £2 rather than £1.50 would kill demand? I agree that increasing demand in the outer zones makes sense as that is where there is spare capacity.
It has always struck me as odd, however, that you can ride around Zone 1 and 2 for £7.20 when the single fare is £2.40 and there is limited spare capacity but if you made a large number of journeys in outer London without entering Zone 1 you are charged to enter it. Raising the Zone 1-2 cap would seem an easy way to increase revenue.