There are differences in views here. Firstly, chapter 11 indicates that Emma does perhaps occasionally manage to get away, or has in the past:

...it was therefore many months since they had been seen in a regular way by their Surry connections, or seen at all by Mr. Woodhouse, who could not be induced to get so far as London, even for poor Isabella's sake...

Since JA specifies that Mr Woodhouse has not seen the Knightleys, rather than saying that the Woodhouses have not seen the Knightleys, this implies that Emma has seen them - perhaps a trip to London to purchase a handsome wedding present for Miss Taylor?

As it happens, though I am biased, in the debate between Emma and Mr Knightley on the topic of Frank Churchill, my feelings are on Emma's side more than on Mr Knightley's. I think Frank should come to visit his stepmother, but I also think Mr Knightley is being a bit ridiculous here. I am on Emma's side when she says:
"I rather doubt that. You are very fond of bending little minds; but where little minds belong to rich people in authority, I think they have a knack of swelling out, till they are quite as unmanageable as great ones. (chpt 18)

I think Emma's arguments have some merit to them.