I have had the same experience. I have used three different turnkey assembly houses that import the native Kicad files, none currently support v6.
Why not just use gerbers? For full turnkey assembly, the XYRS is also needed along with the BOM. Since these full-turnkey assembly houses read the native Kicad board files, it greatly reduces the NRE and therefore total board cost. XYRS and BOM formats are not standard, thus requiring translation either by me or by the vendor. Most automated full turnkey assembly houses take Eagle, Kicad, ODB++, and Altium.
Why aren’t they moving to support v6 if they had v5 support? Of the two full turnkey assembly houses I have talked to, they have prioritized support of IPC-2581 ahead of Kicad v6 support. I understand why they would do this, instead of keeping up with each CAD tools latest changes. Ultimately, this is an artifact of not having an industry standard for the full board package, but it sounds like everyone is betting on IPC-2581 moving forward.
As someone who uses Kicad for commercial development. IPC-2581 support is now the single feature that would make the biggest impact on our workflow.