It IS about the cost, or more succinctly: cost constitutes a significant factor in consumers's buying decision. Stadia is very accessible precisely because of its low comparative cost ($0/mo or $10/mo USD). Not only does this not require a sizeable up-front expenditure, it also carries a reasonable competitive cost amortized over the lifetime of an upgrade cycle, and is arguably much, much more convenient.
And I think you're mistaken to assume that a product must meet the needs of the majority of the market to be successful. This is a fallacy that often prematurely stifles business endeavours. A product need only turn its owning company sufficient profit, and I'm sure Google is well aware of, and satisfied with the state of telecommunications now and/or in the projected future, and that it will support its investment in the product line. Simply put, I doubt that they would release such a product, at such a scale, unless they thought it would make money.
And hey, Google is not alone in this: Sony has already had success with its streaming service Playstation Now (despite sparse and exceptionally negative media coverage) and are likely going to upgrade their service (reports of Sony purchasing server time from MS) and Microsoft is launching its streaming service xCloud. Other players like Ubisoft also are streaming on Nintendo Switch which may see a broader distribution down the line.
Why would these companies move so aggressively if they were concerned with bandwidth? I think that game streaming is viable and that OP has the right idea.
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