There will be people who will take advantage of a day out on very long routes for £2, but will there really be huge numbers of people doing that in January? The £2 bus fares will especially help people wanting to make normal day to day journeys, on routes outside of the large urban areas, where fares can be very high even for a short journey.
I plan to do that, if the £2 fares are available on the longer distance routes from my town. It will be a cheap day out which would otherwise have either been done by car or not at all. Provided there's capacity on the bus, which is likely, what is the harm? The operator receives a fare that they would not otherwise have received, and it takes a car off the road. And there will be a wider economic benefit as I will probably spend money on lunch and in shops while I'm out.
And this might encourage people who don't normally use the bus to give it a try. Some of these people may stick with the bus when the fares go back to normal which would be a positive impact and help to maintain the viability of services.
I wonder if some people will look for the longest route, buy 2 X £2 singles (£4 return) as this maybe cheaper than heating the house for 5-6 hours in the middle of winter…?
Some people might - we do hear of pensioners going out for the day with their free bus passes as a way of keeping warm (which is a disgrace but that's for another topic). On the other hand, if someone cannot afford to heat their house they probably won't want to 'waste' £2 on bus fares. I think most people in that situation would find a local library or somewhere to sit and keep warm rather than riding on buses.
And the fares charged by Stagecoach and Arriva for singles and returns can be different - a feature of deregulation!
It's things like this that put me off using buses when I visit other parts of the UK. Sometimes finding fare information (and how to pay, i.e. contactless, download an app or pay with cash) can require research.
A benefit of a standard £2 flat fare would be people would be confident about how much their journey will cost, which its self could encourage ridership (although would be even better if, like the railways, there was a single national source of accurate timetable and fare data, and a single ticket buying app!)