Delta Color Compression (DCC) was a new feature added to GCN 1.2 (Tonga, Fiji, Carrizo). HyperZ, fast clear and MSAA color compression are older technologies (all introduced before GCN).
DX11/DX12 drivers use resource flags to determine whether a render target can be a shader resource (sample / load). There is no API for the game developer to state whether they want inferior compression or a decompression step (for RTs that are also shader resources). The driver likely defaults to inferior compression, but (driver) application profiles of course could be used to override this. If we had GCN 1.2 on a console, the game developer would benchmark each option and choose the fastest for their use case.