Game streaming could be the way of the future. The concept of game streaming is that most of the hard work is done remotely which reduces some of the bottlenecks that gamers face, which is on the hardware front where some gamers might have less than ideal experiences due to lower-end hardware.
However, in turn, this creates another problem: a stable internet connection. With Google Stadia, it seems that maybe Google isn’t quite confident about mobile internet just yet, and that if you plan on playing games on Stadia, the company will require that you be connected to a WiFi network.
This was confirmed by Google hardware chief, Rick Osterloh, during an episode on The Vergecast. According to Osterloh, he stated that Stadia will require WiFi to work, at least at launch. This means that eventually, Google does plan on rolling out support for mobile internet, but for now, you can only use it with WiFI.
It is possible that Google could simply be looking to test out its service where they want to see how well it handles, and then maybe make some tweaks so that it can be better supported on mobile internet. Currently, on the Stadia page, Google notes that a connection of 10Mbps or greater is recommended.