You've got to remember that AMD are behind at all aspects of this, including documenting their work in an easily digestible way.
"Support" means that the card is actively tested and presumably has some sort of SLA-style push to fix bugs for. As their stack matures, a bunch of cards that don't have official support will work well [0]. I have an unsupported card. There are horrible bugs. But the evidence I've seen is that the card will work better with time even though it is never going to be officially supported. I don't think any of my hardware is officially supported by the manufacturer, but the kernel drivers still work fine.
> Meanwhile CUDA supports anything with Nvidia stamped on it before it's even released...
A lot of older Nvidia cards don't support CUDA v9 [1]. It isn't like everything supports everything, particularly in the early part of building out capability. The impression I'm getting is that in practice the gap in strategy here is not as large as the current state makes it seem.
[0] If anyone has bought an AMD card for their machine to multiply matrices they've been gambling on whether the capability is there. This comment is reasonable speculation, but I want to caveat the optimism by asserting that I'm not going to put money into AMD compute until there is some some actual evidence on the table that GPU lockups are rare.
[1] https://en.wikipedia.org/wiki/CUDA#GPUs_supported