My take is indeed probably more cynical and you're very correct about Delaware being well-trodden, but it does raise the question why the FAQs mention a bunch of well known corporate tax havens [0](Cayman Islands and Singapore) and not other well-trodden territories such as the UK, which has a really straightforward and efficient ecosystem surrounding startup law and incorporation (SeedLegals etc.) and plenty of history to extrapolate from. Also the FAQs mention nothing about having to be in Delaware, perhaps they should be updated?
Its so investors can leverage the massive tax breaks available when investing in US based startups. Hence why YC also lets you found in tax havens like the Cayman Islands. Note this is probably not the official reason, as it's generally frowned upon internationally to encourage tax avoidance.
[0] - https://www.ycombinator.com/faq#q25