There is a difference between reuse and recycling. Reuse is using a container again without major modifications. Recycling is transforming a container into its core elements and using that to make an entirely new object.
AFAIK industrial reuse of plastic food packaging isn't done anywhere because of the risk of bacterial contamination. Many plastics are designed for one-time usage and are difficult to clean. For example the small opening of plastic bottles hinders proper cleaning and the low melting point of many plastics makes sterilization impossible. At best food plastics are recycled by the industry or reused by people for different purposes (e.g. plant containers, toys, decoratives)
I'm not sure what percentage of food packaging could theoretically be recycled into new food packaging, but I do know why achieving a large percentage is currently not possible.
The reason is that plastics used for packing food are required to be of high quality in many countries. This is called food-grade plastic and is sometimes indicated with this label on plastic food containers:
The main problem with recycled plastic is that it is difficult and costly to assure that it is of food-grade quality. This is because:
- washing and cleaning the used plastics will not remove all contaminants (e.g. food leftovers, labels, glue) which reduces the quality of the recycled plastic.
- non-food-grade plastic may be present in a batch of plastic that is to be recycled due to imperfect separation systems (but this would not be a problem if we assume correct plastic separating by households as you suggested in your question).
- plastic manufacturers have to test that the recycled plastic is of food-grade quality and often need to get new recycling processes certified by certain government bodies. This costs time and money.
Another reason for the low percentage of recycled food packaging is that some types of plastics are not or hardly recycled (e.g. polystyrene). This usually has to do with cost efficiency and/or lack of recycling facilities.
AFAIK at the moment one of the few food packaging plastics that are being recycled into new food packaging (on a large scale, outside of labs) are PET bottles, but I've been told that virgin PET is usually added to get a high-enough quality.
There has been research under which conditions certain types of plastics can be recycled safely and reused as food packaging, but it's been my impression that progress is slow. More information about this also here: