Schema.org is an ontology ("data standard") specifically for marking up HTML so that search engines can more easily extract structured data from otherwise unstructured data. Schema.org is very popular for marking up products (reusing the GoodRelations vocabulary), articles (reusing the rNews vocabulary), reviews, etc. If all you care about is search engines, then Schema.org is the only vocabulary you need to care about.
However, HTML is just one way to share information. As you mention, you can provide an API or bulk downloads. Popolo (I'm its editor) is currently targeting those channels. If you're curious about why standards matter in those contexts, I can provide a longer answer.
That said, even if you only use Schema.org in your HTML, you'll be offering partial support for Popolo, because Popolo reuses terms from Schema.org. It also uses terms from predecessors of Schema.org that Schema.org subsequently adopted. For example, Popolo's Person class has significant overlap to Schema.org's.
As for adding Popolo terms to Schema.org, that's definitely a possibility. For example, I think it would make a lot of sense to add the
dissolutionDate property from Popolo to Schema.org's Organization class, so that companies can dissolve like in real life.
Last point: unless you plan to share data with other developers through HTML, as far as I know, there's not much to gain from using vocabularies besides Schema.org in your HTML. If you want to share data with other developers, you should offer bulk downloads or an API, instead of requiring people to parse your HTML (even if that HTML has beautiful semantic markup).