I’m less convinced that vacancy itself tells you much about likely flexibility. A vacant property can mean the seller wants a quick, clean transaction, but it can also mean they have no onward chain and no reason to accept a weak offer. An occupied home may have a much more motivated seller...
I’d add a caveat: a promised fast reply is not the same as progress. A provider can answer within hours while leaving negotiations or paperwork unresolved.
Ask what happens when the assigned person is absent, an applicant withdraws or the purchase is delayed. The fallback should be operational...