Most government health rules and regulations do not go so far as to specifically make Aprons compulsory to wear but nearly all require clean protective garments to be worn in food preparation areas and when handling food.
While other clothing including smocks or lab coats may be technically acceptable, aprons are a cost-effective, convenient way to be compliant.
Especially for businesses that do not have laundry services, locker rooms etc, the apron provides some comfort and protection against soiling and contamination.
The Chef Aprons serves as a barrier to prevent micro organisms to some extent, but especially physical contaminants like hair, dust, and dirt from transferring to food.
In terms of which employees need aprons, regulations also vary but generally would be anyone who handles food or works in a food preparation area including people who are not handling food like dishwashers.
Another group of people who need to cover up for safety is medical personnel when handling patients doing blood work etc.
Scrubs are a suitable cover for this type of work.
Aprons are a food safety tool but like any tool, they need to be used effectively to work and to also choose the right apron for the job
They need to be clean, changed frequently, removed before leaving the kitchen or using the restroom, and should be worn over clean clothes.
Disposable aprons are also acceptable and these days there is quite a variety to choose from.
With the styles, fabric, colours and designs available now there is really no excuse why staff cannot have a smart looking apron to go with their uniform and be comfortable to wear.
As always, the best authority on the topic is your local health department as they will be the ones enforcing the regulation.
Your local Hospitality association may also be a good resource on this topic.