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Many people have a warped understanding of what "two factor" means.
They conflate it with devices and they think it means that one of the factors (why one? which one? who knows) needs to be restricted to exactly one device.
What "two factor" really means is that you should have more than one required factor of authentication so that if one is compromised the attackers still can't get in.
Ideally the factors should be spread across the "something you know" / "something you own" / "something you are" categories to complicate the manner in which they can be compromised.
We can only reliably rememeber a limited amount of passwords, so like it or not we have to use some devices at least some of the time.
The trouble with "something you own" is that it can be lost or damaged or stolen, and if you only have one of it then you're fucked. So adding some redundancy is not a bad idea.
The larger issue is that everybody is stuck into extremely rigid and outdated mindsets that date back decades. "Two factors" don't have to be exactly two, and they don't have to include exactly one password, and so on. It should be fine if you wanted to secure your account with 3 passwords, and should be up to you if one of those password is a barcode tattooed on your taint so you need a mirror and to bend upside down to scan it.
Bottom line, use whatever you want and use your best judgment as to how secure is each factor. If you want to use something that syncs to multiple devices, go ahead. What you should consider is who has access to those devices and how it would affect you if they're lost or stolen.