I guess because no-one really owns it as such? It's within the purview of the Rail Delivery Group but that means it's very arms length from the TOCs that actually deliver the railway services which National Rail is intended to be informing people about. It also means that there's almost certainly not much money available to spend on the website itself and developing an app for the service.
And why should there be? The TOCs do their own apps (with varying degrees of success) and their own websites as well. It's not in their interest to provide money to RDG to upgrade National Rail, they've got their own patch covered by their own apps and websites. Why on earth would they contribute to a third party app/website when the benefit to their own services is negligible? After all if your a customer of TOC X why would you not just use TOC Xs website/app (from their point of view)?
I would hope that this is something that GBR might get to grips with either via the National Rail branding itself or in a new GBR form. It seems beyond obvious that there's a need for a proper do it all app/website, which is given sufficient resources to actually deliver a good service, for the railway network. But on the structure we've had since the 1990s it seems quite obvious how we've ended up with the rubbish we've gotten via National Rail.
Looking at the accounts of "Train Information Services Limited" they have spent £5m on software development over the last two years, presumably mostly for the website rebuild. It's a decent chunk of money, though again far less than Trainline which is upwards of £30m per year and Trainline would use permanent staff with lower cost as a result.
The financial motivation for a better central railway website is clear, taking even a percent of Trainline transactions back onto TOC websites via National Rail is a significant sum (back of envelope maybe £1m per year). That's why one of the focuses is the shift to promoting tickets over plain journey planning queries as that's a key success target.
With only info in the public domain, I'd be inclined to agree that the structure being a likely part of the problem. Even though they had the cash to do something it's not a situation the organisation would be used to. As well as having to procure a solution at higher rates than permanent staff, they needed to run a procurement with a product mindset they wouldn't have done recently. Formal procurement can be challenging as being good at winning procurement processes doesn't necessarily mean good at delivering the end product. If the supplier chosen isn't great it's hard to get rid and reselect compared to the 'full' private sector. They also wouldn't necessarily have enough people or people with product development experience to assist the supplier and challenge any assumptions. Stakeholders may have jumped out of the woodwork with feature requests and demands as see the only chance to get their pet project implemented as there's only one pot of cash.
I'd expect as part of GBR someone to step back and look at what intellectual property is now publicly owned then look to consolidate. Not all TOCs will be the same, however the London commuter TOCs or intercity TOCs could all use the same solution with different branding. There would then be the question of what the central National Rail website should be trying to do, making it sell tickets without a handoff would reduce friction. The consolidation would hopefully allow less money to be spent while providing a better overall experience, I wouldn't want to bet on it necessarily working out though.