Of the numerous cases where I have seen this done, there generally is no problem. While uniform sand has weak shear strength, it does not compress noticeably.
However, one case with saturated sand that replaced a silt undercut, followed by a saturation of that sand in a "bath tub", the sand flowed out from under due to the weight of the footing, column and roof steel only, but also due to running of plate compactors nearby, helping the sand to flow. With no nearby vibration, it did not flow.
The cure was interesting, in this industrial building with the footing measuring 8 x 8 ft. Roof was not on, but steel was. A crane picked up the column and roof steel a little, leaving the footing free. A dozer shoved the footing off to one side.
Saturated sand was dug out and replaced with damp sand, compacted.
Footing was shoved back in, at proper grade, wiggled back and forth to "seat it", and column re set. All worked out fine.
You don't always have to discard compelted work.
Oh yes, on the same site, dry sand did flow out from under the foundation of a large air compressor. However, that compressor did so much shaking that nearby precision testing of machines also was affected by the shake. This was a most unusual situation, not common.