I just checked the first of my rail journeys for the next trip, Manchester Airport to Skipton. The ticket price is the same whether it's purchased from Transpennine Express or from Trainline. The latter charges a £1.02 booking fee for a £34.10 ticket. If you're traveling around enough to use several rail companies and you order tickets in advance from those companies, can you pick up all of your tickets from the same machine? I like to have all of them in hand at the start of my holiday, and I avoid having them on my phone. The rail companies won't mail outside the UK, and lately Trainline doesn't, either.
The only ticket I've ever tried to carry on my phone was a National Express Hotel Hoppa ticket from any LHR terminal to the Premier Inn on Bath Road at the end closest to T3. I activated the ticket while I was inside the terminal and had good Wi-Fi. By the time I got out to the bus stop less than a minute later, the ticket had vanished. I went back inside to re-access it, and the system told me that it was no longer available. I was out only £5 on that one, but I'll never put a ticket on my phone again.