I got my hands on a Samsung Galaxy S7 to try it out. Lo and behold, it works perfectly fine there.
jordanjay29 : So it looks like the issue is with iOS, regardless of browsers. I did a little more research as to why both the browsers behave the same, and found this little piece of information
“Chrome for iOS is derived from the WebKit browser codebase, as is Apple's Mobile Safari. However, while Apple allows only Safari to access iOS facilities like the iOS Nitro engine, Chrome uses Apple's UIWebView for loading and rendering content.”
So it seems there are two distinct issues here, and both belong to iOS:
The text area not being activated automatically and ready to take input when you hit reply.
The text area going out of view the moment you type any character.