It's not all about memory footprint; it's sometimes about just working for the grandmother who buys a $35 Chromecast from Best Buy.
And sometimes it's not all about that either, but about vendor lock-in.
Sometimes "making it just work" and "avoiding vendor lock-in" are incompatible. Plus, it's literally called "Chromecast."
The device itself runs chrome. So I don't think of the sender as the influence in the name. Plus chrome has a good mind-share which helps marketing.
Is it vendor lock in if you're casting services like Netflix etc? You can use many different devices to watch your content. We've had a Chromecast since the first version and it has always worked well (with the exception of Netflix lately). I recently purchased a Sony Blue Ray player and was surprised to find Chromecast built in to that.
What he's referring to, is that without the extension, other Chrome-extension-compatible browsers are not anymore usable for Chromecast. You now have to use Chrome.
Couldn't they just have the extension pre-installed with the ability to remove?
Then you get people hating "bloatware" and complaining.