Arguably, if you could get from the Channel Tunnel to Thurrock (i.e. North of the Thames), you could remove the need to build the Lower Thames Crossing whilst still cutting congestion to the existing crossings for other road users.
There has been (possibly still is) a container service on HS1 to Ripple Lane, where UIC-GB clearances allow the transfer onto roads. However it's problematic for taking up space from the HS services.
Whilst it would almost certainly be more costly than the Lower Thames Crossing, the likes of Kent have been saying that in a post Lower Thames Crossing world there would be a need to upgrade more of the Strategic Road Network (SRN) between the crossing and Dover. It's also likely to mean more maintenance across the SRN. As such it then becomes a question of does building the rail link then start to be better value for money, especially given the environmental benefits it would also bring.
It could also shift the economics of if it's worth sending a driver and cab with the trailer, not a lot but maybe enough to make paying to use rail a little better than not. Which, may in turn shift a bit more to being containers.
Tbh if you're building a new line to rolling road size, you'd want it to go to Daventry at least, so that trucks can get onto the M6 for the West mids and M1 for the East mids.
Maybe there is a binary choice between mass private motoring (hence much road capacity and thus the adoption of larger and larger hgvs) and mass railway provision( both passenger and freight transport).. And that choice was made in the last century.
It's not a binary choice though, it's a specialisation of what each is good at. Rail is king for commuting into large cities, and moving big bulk loads, or long distance loads where the higher speeds can mitigate the time lost in loops and whatever. Whereas roads are flexible, accessible and have a high availability.
Trunk loads of freight run on core corridors, and significant money has been spent maximising these corridors. But look at Rolling Roads elsewhere - how many HGV services exist outside of significant natural barriers that makes building a highway vastly more expensive than running a freight train?
I think a reasonable case could be made for a freight line allowing the Essex Thameside area to bypass London to get to the WCML, but that's probably the only one. Even the Dutch, with Rotterdam, only built the Betuweroute recently and it hasn't been a stunning success because it couldn't easily interwork with the existing network.
