One question, is it *likely* that signalling a desire to have the case heard will result in a hearing? Obviously, it’s understood that signalling this opens up the possibility.
It increases the chances of a hearing, which is one of the reasons it increases the chances of them discontinuing.
If you opt for an in-person hearing and they proceed, they'll have to spend the money to send someone to your local county court to argue their case. If you agree for the case to be heard on the papers, this suits the claimant, as their solicitors can simply submit written evidence and have the matter decided by a judge without them having to turn up.
In other reading I’ve done on the matter, mediation is often described as the eventual endpoint.
Mediation is only the endpoint if both parties agree to a settlement, which, given your position is that you owe nothing, is unlikely.