If this is the reason (I don’t believe it personally) then there should be no problem with an outright ban on non-compete agreements for zero-hour contracts. Somehow I don’t think employers will agree.
Non-compete agreements (or any clause restricting working elsewhere) are generally not enforceable in UK zero-hours contracts. Explicitly since January 2016, and in practice before then.[1]
nickdothutton|3 days ago
[1] https://www.gov.uk/government/publications/zero-hours-contra... (Bottom para.)