We have done in the past. On doing supplier re-approval and supplier performance monitoring it became apparent certain companies were lacking in providing adequate traceability in reasonable timescales. They were issued non-conformances in turn. They were warned that failure to comply in loss of business, 3 out 4 suddenly complied. The 4th didn't and were removed from approved supplier list. That was £100,000 of business lost for them.
It was a painful exercise as the buyer had to use a slightly more expensive supplier and in turn put pressure on us as a department. We stood firm on the issue and haven't looked back.
If our buyer looks at new suppliers of anything he is now very aware that they need to comply with all requirements not just price, availability and terms!
P.S as a default, where applicable we try and ensure that they BRC or equivalent approved before anything else..........makes life so much easier. Plenty of suppliers wanting your business one would hope :)