It doesn't matter if you store your 2FA seed on a billboard or as a tattoo where the sun doesn't shine: 2FA means two factors. The definition doesn't change when your home setup's threat model doesn't call for 2FA and you thus decide to store two secrets in the same place (making a compromise of one necessarily a compromise of the other, thus 1FA)
The only necessity is logical necessity, and it doesn't apply there.
But if its on the same device, it will not protect you against a password database harvester.
Something that you have can be your own pc.