Doubtful that restaurant owners would want to entice the customers that testing would bring. The current customers would go elsewhere.
Tests take a substantial amount of time. Door staff could be tasked to check the results of self-administered tests, but monitoring their execution would be far too demanding. Expecting them to be able to administer them in a controlled way is unimaginable.
Anything self-administered is open to gaming by the customer.
Anything administered by venue staff is open to gaming by the venue itself — whether it is protecting scarce revenues, or just treating valued customers differently.