Where specifically did you see stadia advertised or shown off for mobile LTE? They're deliberately avoiding cellular data.
And the people with gaming PCs going on and on how stadia won't replace their gaming PC are also not shining a light on anything unknown.
They are aiming squarely for the living room console demographic, that's really all. The people that may play in a browser are secondary.
And I'm sure all the bad word of mouth of this fucked up launch is going to go wonderfully with the living room crowd. Also, no one seems to have an answer as to how exactly Google plans to entice the console crowd away with a service that forces them to re-buy all of their games (at shitty prices) and forces them to not play games with any of their current friends unless all those friends also happen to get on board. The free option isn't out until who the fuck knows when so they have to pay $130 + $10 a month (admittedly after three months) to get a worse experience (up to nearly 60ms increased latency based on Digital Foundry's preliminary tests) and play with less people. Sounds like a real fucking winner right there man.