It's a nice idea, but Rail is about bulk transport, and parcels are generally not moved in bulk. In the living-with-COVID world, the additional complexity of having to ship everything from the stations to home addresses means it's a non-starter. Had it survived, the Doddle parcel pick-up service could have provided some form of infrastructure for a limited express parcels service. It might have been feasible for trains with a 2nd person already on board to have a secure compartment where pre-booked packages could be stored. At stations Doddle staff would be waiting to meet the pre-determined trains, and by offering the station pick-up point as a general service for all Click & Collect it might have been able to offer commuters a useful option to pick up items on their way home. But with COVID it would have died anyway.
In the post-COVID world, we are likely to see home-working remain a substantial part of many people's employment. So waiting in for a delivery driver isn't as inconvenient as it used to be (companies are being more flexible), and people aren't passing through the station every day like they used to. With the rise in orders, deliveries can be allocated in more optimal patterns to allow efficient drop off, so the benefit to the vendor is less. Parcels & mail have a place on trains, which already operate for Royal Mail: dedicated, fast, bulk flows.
On having dedicated staff travelling with the train I think the fact that the railway needs to reduce it's costs to survive post-COVID would prevent that. Also if you use existing stock you'll need ramps on board for your trolleys to get on and off. Dedicated postal platforms are higher than standard (look at Stafford for an example) and have ramps stored on the platform edge for loading/unloading the trolleys.
There was a (theoretical) chance of late-night Intercity trains carrying next-day packages at a premium. But I think the AT300 derived trains now (or soon to be) dominant on the likely routes don't have a secure space, and the issue of shore handling would still need sorting out. The problems could be overcome in engineering terms, no doubt, but the financial and operational issues are far harder to resolve.