How is entering a number and saving it to your account “painful”?
They're reasonably long numbers, people will get them wrong. You'd be surprised how many people struggle with the basic concept of copying and pasting something without a introducing additional characters. If they've bought the Railcard from you it's easy - because you already know the number without needing them to input it. That would be great if you could sell every type of Railcard, but you're not allowed to; of course.
Not everyone will have an account with the retailer - I can tell you the proportion of guest bookings is much higher than you might expect. People don't want to remember yet another username and password, and not enough people use a password manager. Perhaps you want to encourage behaviour change here, but the first site that rolls this out will be at a disadvantage to everyone else who hasn't implemented the requirement. It will also disincentivise people switching retailer, because they'll have to set-up their Railcard preferences again. Ideally any new requirement to need this input before buying tickets would be rolled out across every retailer, including TOC retailers, at the same time. That's not exactly easy to coordinate.
The Railcard number will need to be validated, which takes time. The validation service may not be available 24/7. There is an open question as to whether that needs to be done in realtime or not.
When should the Railcard be revalidated? They can become invalid after purchase. How often should they be rechecked? Should tickets be cancelled if, after booking but before travel, the Railcard is no longer considered to be valid?
If you try and validate names, the names in the Railcard database likely won't match the ones on the account for a variety of reasons. Is that a showstopper, or do we not care about name mismatches? If we don't care, what stops people sharing Railcard numbers around? Should we limit the number of accounts that can use a particular Railcard number? Who will be responsible for storing the data of existing accounts associated with a Railcard?
If you require this online, you should also require this on TVMs so the playing field is level. How will input of Railcard numbers work there? The keyboards are awful to use, and people won't have a "TVM account". Should we introduce one, and require people to remember to "logout" of the TVM? Or perhaps we should retrofit Aztec barcode readers onto every TVM so the number can be read out of a Digital Railcard barcode. What about customers with a plastic Railcard?
It's very easy to oversimplify this into "just type in a number and save it into an account", but the reality is much more complex than that.
I am not saying I think the answer is "Do Nothing" or that there is no room for improvement, far from it - but I've already done quite a bit in this space to try and improve things and the industry collectively has grappled with this on numerous occasions in the past.