I think the website is missing important information (or it's buried somewhere):
- quick facts about Pitcairn [0] (e.g. 47 people, 47 sq.km of surface, British Overseas Territory)
- what kind of visa you will grant (permanent resident?)
- is there a path to citizenship / passport, and if so, how long it would take?
- is there any special agreement with the UK? e.g. UK passport after 5 years of residence.
- income tax? capital gains tax?
- how easy is it to setup a business in Pitcairn?
In any case, I plaud the effort to try to repopulate this island.
There's something about human communities where under a certain size (200? 1000?), many things become really difficult, such as having key expertise "in house" (doctor, mechanician, electrician, plumber, etc), as well as being able to maintain a good "vibe" in the community.
My guess is that 47 people on a 47 sq. km island are a bit on the low end. Hopefully they will manage to attract more people over the years.
They might want to consider asking a government (UK? New Zealand?) to help them with some budget and an immigration program that could easily attract at least tens of people.
[0]: https://en.wikipedia.org/wiki/Pitcairn_Islands