IMO, diversity of abilities is far more important in most workplace than diversity based on things like sex/age/country of origin etc. It's invaluable to have different people with different strengths to bring to the table. You can have 5 employees all doing the same job working on the same project, but with different talents/strengths and having those recognized and taken advantage of you can create some amazing things, everyone will look at a problem and have different great ideas to bring to the table that will add up to success.
Sure, but you won't get that insight until someone has been on the ground for awhile.
Diversity based on gender/race etc. can be valuable as well because different groups see the world through a different lens and bring those different perspectives to the table, but that would depend on the type of work too. ie: having group diversity within a roadwork crew isn't going to have much benefits compared to in an HR office.
There's not really much value other than it shows your firm doesn't limit hiring and it opens up the pool of opportunities you can pick from. My industry is different in that we are always very much looking for people and can't find them. It's not like the proverbial new Walmart that has 1,500 people who apply to be a door greeter.