I do not know if it's true for all countries, but at least the USA and the UK require your passport to be signed to be valid. And I know that when I fly, I sometimes get checked if it is signed.
Is there a practical reason for this? Does the signature get checked against anything? Or is it simply that the law says a passport must be signed to be valid, so there you go?
I googled around a bit, but only found resources on how to sign, but not why it needs to be signed.
The theory is that you've signed your passport and it's on a type of paper that will visibly deform if you try to erase it or white paper over it - so in theory a border guard could ask for your signature and compare it to the one on the document as a proof of identity.
In the modern world this doesn't really matter because we've got a lot better ways to authenticate - including databases with your signature already in them.
However, the tradition lives on.
Oh also, it's always a good idea to get someone to sign something if they're doing fraudulent stuff - since it's absolutely trivial to prove a forged signature done in front of a witness in court... it's like getting Capone for tax fraud - easy to prove cases are easy.
I personally have a signature stamp. I imagine that would work for anyone who has literally any range of motion, down to "can hold a stamp in their teeth and tilt their head a few degrees to press it against a document".
For people who don't have even that, I think a notary is allowed to sign on your behalf, if they can be provided documentation of your disability, but that will vary by country of course.