Hi,
I don't think it depends only on institution policies. It depends on training.

A Physio degree as well as a Nursing degree should include training for oral and nasal suctioning; in your clinical placements you should then be given opportunity to practice. If not, there should be on-site practical training in your department, when you are actually required to work in that area. We get yearly updates, as guidelines and equipment changes and as we don't all work in the area every day, but are on an on-call rota.

If you are trained but not permitted to use your skill, it would be worthwhile to get your manager to discuss this with hospital management. I would see that as part of their responsibilities.

Airway fitting and Suctioning is a skill; it is potentially dangerous - you can cause trauma, oxygen mismatch, infection and more. So, there is heaps of precautions and certainly a skilled pair of hands (if not 2) required. For safety precautions, if somehow possible, I would always have someone on site, as well.

Regards,
Fyzzio