... and this is exactly why I do not like this at all. I still need to have 2 or more computers.
That's, like, the whole point of 2FA.
I'd say using a separate program on the same machine offers some additional security over not using it at all. A simple keylogger won't compromise your account anymore, though anything that can just read the 2FA files can, but I'd hope those are less common so far.