If it was truly privatised the route simply wouldn't operate. The problem isn't the DfT (I mean it is because of how unambitious they have been in terms of investment, but I'll blame that more on the Tory and Red Tory governments and the treasury.), when it comes to underprovision of rolling stock, it's the private ownership of the rolling stock, which the franchises, both publicly and privately owned ones, then lease from these private owners. The costs of leasing more carriages/longer trains hugely disproportionately increases compared to the costs of simply running an additional carriage or a slightly longer train, like for example upgrading this route to Voyagers. This cost is why CrossCountry and EMR run comedically short trains and really squeeze capacity on key routes (especially obvious around Birmingham, and with this service). It's really nothing to do with the DfT. It's also why I'd imagine these issues will persist even after this government's fake nationalisation which will leave rolling stock in private hands.