The nice thing about booking direct either online or via the app is you don't need to know every single delay repay rule. You get an email telling you that you are entitled to compensation and all you have to do is click on the link. The rest is automatically taken care of and the credit is then put back on the card you used to pay. You don't have to do anything else.
This has happened to me numerous times and no mistakes were ever made.
I always feel that for tourists sometimes ease of use is the most important thing. While some people still prefer buying physical tickets, which is a perfectly reasonable thing to do, a tourist might look for the ease of things especially since they have so many other things to think about.
I'm the type of person who buys direct from the supplier when it comes to travel--air, hotel, trains, etc. Less hassles if something goes wrong. And when you travel full time like me, the less hassles the better.
Train travel in the UK is getting busier and busier. I have been on trains where it was standing room only. You will get allocated a seat regardless of the train company you book with.....however.....for a family that doesn't mean you will sit together. If the train is already fairly full, they may not find the number of seats you need together. Or a seat at all. Tickets will be sold even if all seats are taken.
For a person traveling alone, this isn't a problem if they are willing to sit anywhere or stand anywhere. But for a family?
I remember taking a train from Penzance to Bath a number of years ago. (I changed somewhere but I don't remember where.) One of the trains was so busy, literally every place to stand was taken. (And this was in May.) June can be busier.
It's your call, do what you think is right for you.