Clarification: No room for 4 offered on points (including cash/points upgrade) when (non-suite) room for 4 available via cash.

I know this is common in Europe (rooms don't handle 4), but I was surprised to find that the JW Turnberry in Miami doesn't offer a room for 4 on points, even with a cash upgrade. They offer a king room on points, but that's it; verified it via a "1 night stay/flexible" with no availability ever and also via the Titanium line. Very odd for a hotel that includes a water park, although I imagine they sell out regardless. Are there other similar points-family-unfriendly hotels that offer a paid stay for a family of 4 in a single room, but not a points stay?