This is not a Linux problem; Windows 10 would fare way worse. Maybe similar on a Pi 5, I've seen a review and it handles Full HD on either OS (only Linux can get consistent 1080p60 though).
I have a Pi5 hooked up to my living room TV and it does indeed play 1440p60 with zero issue. The OS is a bit laggy getting into the video, though. I want a case like I have for my Pi4, a case that allows for a built-in SSD.