... 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.
Yeah, you do gain additional security, since many keyloggers just grab as many passwords on autopilot and that's it. However, if someone is specifically targeting you or uses a more advanced keylogger, they can access the 2FA program just as easily as your password.
Running a 2FA program on your main machine is a bit like using a Mac for security: It's not inherently more secure, but since it's less targeted by attackers, your chance of getting hit is reduced.