No "if", no "would", we are millions of gamers using our (portable) PC with SteamOS running on it for few years now already.
As others have pointed out already, the SteamDeck is exactly that. I even travel with it, use desktop mode with my BT mouse&keyboard with a USB-to-HDMI adapter and work on large screen and do my presentations with video projectors.
If they were to sell a desktop too... well I have a Corsair ONE already, naming a gaming desktop (2080Ti) with a very small footprint and relatively silent. It is not easily upgradable due to how compact it is (but can be done) so if I were to have an equivalent of it from Steam and they were to keep on contributing to FLOSS it would probably be an even easier buy because I trust their RMA and I imagine I wouldn't pay a "Windows tax" with it as it would "only" come with SteamOS.
I had an alienware Steam Machine and it was perfectly fine.
I think the criticisms of the Steam Machine suffered from what I would call the Verge Syndrome, which is only being able to comprehend things in a binary of instant success or failure, with no in between and no comprehension of other definitions of success.
Steam Machines were a low risk initiative that were fine for what the were. They did not have a ring of death, they didn't have a blue screen, the OS itself was not glitchy, they didn't lose money, and they didn't fail any stated goals. They got the Proton ecosystem up and running, and got the ball rolling on hardware partnerships, which led to the smash success of the Steam Deck which would not have been otherwise possible.
I am sure they were fine machines. I don't think they were profitable for Valve (that is what I meant with "not worked out well"). On the other hand, the Steamdeck might not exist without the Steam Machines, so maybe I am wrong and it did work out well.