It's apparently not unusual for the deadline to be missed - writing a comprehensive witness statement that contains everything that's relevant to the case can be a bunch of work. What normally happens is that one side asks the other for an extension and they agree. If that doesn't happen, it's possible to ask the court to extend the deadline instead. If the court agrees, and if it appears that the refusal of the other side to agree was unreasonable, you can get costs for that application.
If you file a case and then serve no witness statements, you're not going to be able to provide any evidence to support your case and you're unlikely to get very far. Similarly, if a case is filed against you, and you fail to file a witness statement, you're not going to be able to provide any evidence supporting your defense at trial and that's largely considered a bad thing.
But fundamentally a witness statement is just a written description of the evidence in the case. If you want to be able to testify, you write down what you want to be able to say, sign it, send it to the other side at the appropriate time, and that's it. There's no cost associated other than time.
However, while a witness statement contains the evidence you would like to testify about, you still need to be able to provide that evidence at trial. There are provisions for this to be done by video, but judges apparently prefer not to, and there can be complicated legal issues around whether someone's local laws in a foreign country allow them to be sworn in. So the typical expectation is that witnesses be present at court, and there is potentially expense associated with that.
Still: asserting that you have 6 witnesses willing to testify, then filing witness statements on behalf of 0 of them, and then not filing witness statements for yourself either, means that you are not going to be able to present evidence at trial and all you're going to be able to do is try to undermine the other side's evidence.

This turns out to be a particular problem if you're, say, involved in a defamation case in a jurisdiction where you're required to prove that what you wrote was true. If you can't provide any evidence because you never filed any witness statements, that's going to be something of a challenge.

(Yes, the burden of proof being on the defendant is a somewhat fucked up part of English defamation law)

@mjg59 How does it work when you're being questioned by someone trying to undermine your evidence and you realise you need to explain something that wasn't in the statement?
@penguin42 CPR 32.5(3) allows the court to give permission to go beyond what was in the witness statement
@mjg59 The fact that you're telling us all this in great detail makes me assume that _someone_ did not do that correctly...
Dr Matthew Garrett v Dr Roy Schestowitz & Anor - Find Case Law - The National Archives