Yes. I could see a simple "Statements" vs. "External identifiers" distinction being useful that's also reflected in the data model so it's easier to treat these property groups in a distinct manner.
I support grouping statements about external identifiers together and distinguishing them from other statements, but I would voice caution about presenting that distinction as "Statements vs. External identifiers".
I agree with Denny that qualifiers and references should be retained for external identifiers. I would further suggest that external identifiers remain structured as properties that can (along with their values in claims) be created, updated and deleted by the community.
Given that, I think the distinction should be styled less as "Statements vs. External identifiers" and more as "External identifiers as a kind of statement". UI editing controls and data modeling as statements would remain, but "External identifiers" (e.g. *VIAF identifier* 113230702) would be moved to the bottom or side of statements of subject knowledge (e.g. *cause of death* heart attack).
Grouping together and separating external identifiers from other kinds of statements in the UI, and reflecting that in the data model and API, sounds like a great idea. https://www.wikidata.org/wiki/Q42 is a rat's nest of meaningless (but technically useful) statements about external identifiers and meaningful statements about the subject. It's important to fix that, and I imagine we could do so while retaining all the current UI controls and data model attributes of statements in statements about external identifiers.
Best, Eric