This is one of the many reasons why my chromecast was tossed into a box with other junk. Chromecast wants to run through Chrome or no cigar. To get full screen does F11 work or does that only work for PC screens. I gave up on my chromecast years ago very shortly after wasting money on it.
I was going to sell my chromecast to try to get $20 of my $35 back and its associated with my gmail account and permanently bonded to my e-mail. In order to sell it i would also be required to give them my e-mail account, so its a piece of junk to me. Maybe someday it will be worth something 30 years from now to a collector as its in the box with other junk, doesnt take up much space, and I might get something of that $35 back.
For some people the chromecast might work out perfect for them, but not for my home and our needs. I have a Roku model 1 as well as my BluRay player has ability to attach a up to 32GB external drive to it to play movies in FAT32 so i found a purpose for an old 40GB IDE Laptop drive formatted with a 32GB partition with a USB/IDE adapter, as well as I can Plex to these devices if I wanted to using a system as a media server.