It isn't quite so simple. Felixstowe has doubtless offered ocean carriers everything it can to get vessels to divert to Thamesport, but the lines clearly don't want to go there - and it is entirely their decision. Only Maersk have taken them up on the offer with Maersk Kithira, and I think that was essentially because there was no space on the day at Gateway.
But the problem with using any other port is that all of that particular line's UK operation is based in one place - so there's a constant road/rail stream of empty and export boxes, stacks of empties, transhipment boxes from feeders, etc., to be dealt with and to be backloaded onto ships. However, this is more of an inconvenience than a disaster - most lines have several ships a week covering some of the same destination ports, and they often can access container slots on other lines ships.
But imports are different - most import these days is on a just-in-time basis, so if imports are a day late getting to UK factories or shops, those factories can come to a standstill, or the shops have empty shelves.
The one-off calls that have happened at Gateway and Thamesport so far have been unload-only, I understand, and that means that anything due to have been loaded onto that ship from Felixstowe will have to be dealt with on another vessel. Meanwhile, they give Gateway more experience of both quayside and landside operation, and mean that they'll be able to keep improving what they do before berths 2 and 3 open.
Reports currently say that their quayside operations are speeding up, although I haven't heard much about their landside - hauliers and the haulage industry seem to be keeping a little quiet about any problems!