I don't agree with this ban. I also don't understand how a non-judicial US arbitration applies to the UK or in Europe. It shouldn't.
From the book authors perspective, signing the severance (and by definition taking the payout) means you're giving up the rights of disparagement and legal action against the company. This happens a lot of times. For example, if you have a legal employment complaints against your supervisors in a US company and have filed for external legal action, signing severance (if the company lays you off) means you give up your legal action and agree not to disparage company leaders.
The solution here was to not sign the severance and write the book.
Fwiw - I believe severance should be like non-competes. It cannot come with these clauses unless the value of the severance is over some set amount (e.g. above $10m).
I think the publisher should just make the book freely downloadable and distribute it via torrents and any other means.