And as Central Railway would probably not allow the existing FOCs on their track, they would thus be in possession of a North-South route with none of the congestion problems, and minimum speed limits, encountered by current freight.
That would seriously damage the FOC's business models, which means it would be in their interest to kill it.
Conversely, if they thought it was a terrible idea that would never cover its costs they would like it, because after CR go bust they can pick up the infrastructure for a song and solve said national congestion problems.
You have to escape the idea that FOCs want what we want, what they want is to make as much money as possible.
EDIT:
If we were to assume that 40% of the HGV traffic through the Chunnel or coming over the channel ports is heading to places in the vicinity of or north of the southern side of the M25, and that 60% of this traffic could be captured, that would be enough to justify effectively hourly mile long TOFC trains, or actually more trains than that because they would be a mix of TOFC and rolling highway stock.
And this is before we consider the effect of the drastic reduction in rail shipping costs has, or any internal traffic generated by this. (190 TEU with a single driver who has ATO and is thus paid less than regular staff? And this is before we consider that double stack 8'6" containers would already be cleared through to Calais. There may be no container traffic now but there might be if container transport costs were slashed.)
And the reason 9'6" containers are replacing 8'6" ones is that most shipping firms charge th same for either, but if 8'6" can be double stacked through the chunnel but 9'6" ones can't this won't be the case.
And with modifications to the apparently standard OLE in the Chunnel they might be able to fit double stack high cube container trains (using Furrer and Frey Contact Rail type jobs).