On-site is the default modality for any encounter where trust and nuance carry the work. Mental-health assessments, end-of-life discussions, child-protection interviews, IEP meetings, civil court testimony: these are the encounters that depend on an interpreter being physically present in the room.
The downsides are scheduling lead time (days to weeks for less-common languages) and cost (the interpreter charges for travel time and mileage in addition to session time). The upside is uncompensated: communication that actually works when it matters.