Maybe it is for me only but I really careful when explore a new site on my mobile. Because we don't know much about their trust and their website can contain hazardous things which can steal our information on screen, keyboard. My mobile is a device I used to store my 2FA so I don't want it to expose to so many new sites.
I do not think it is possible for a website or app to steal your keyboard information, except your device has previously been infected by a malware or virus. The screen resolution could be used by some sites to bring up pop ups in awkward positions (and make the option to cancel so small), where one can easily click to accept some random suggestion mistakenly as they would by clicking with their fingers.
Not exposing your device to random site is wise and something I also apply in my dealings with gambling websites.
- Jay -