Worksafe said Mr Taylor did not have the qualification and had not shown an intention to get one, despite a deadline of the end of this month.
It was illegal to be operating without the certificate, and offenders faced penalties of up to $250,000.
But policing the $600 million quarrying industry was difficult because Worksafe had not completed its database of operators.
Industry body the Aggregate and Quarry Association also said the scale and qualifications within the industry were unknown.
Labour MP Iain Lees-Galloway said Mr Taylor's death raised questions about Worksafe's resourcing and its ability to enforce existing standards.
The MP wanted a new round of health and safety reforms - currently before a select committee - to class quarrying as a "high-risk" industry, which would mean every firm would need a health and safety representative.
The Government has promised that new guidelines are on the way for the quarrying industry.
Quarry safety
• There are at least 850 quarries in New Zealand, with at least 1200 employees (not including contractors).
• Quarries were exempted from most post-Pike River tragedy safety reforms, but owners were still required to upgrade their safety certificates.
• To gain a certificate, quarry managers are assessed at a private training organisation.
• Quarry owners with no certificate need to apply this month; existing holders need to get the new certificate by January.