There's no back-end complexity issue with multiple 2FA devices. The issue is the trade-off between security and convenience, which is the age-old problem of authentication systems.
The "two factors" in two factor authentication are a thing you know (your memorized secret, or password) and a thing you have (your 2FA device, security key, etc). If you allow the thing you have to be many things, it significantly increases the chances of the thing that you are supposed to have is in the hands of someone else, which eliminates the advantage of having a second factor at all. Especially since the only reason you would ever need more than one device is if your primary 2FA device isn't where you are.
If your second factor device is a device with biometric capability (in other words, the fingerprint scanner on your phone), then your 2FA software of choice might use that to introduce a third authentication factor, a thing you are (your fingerprint, iris, voice or any other biometric measurement can be considered a thing you are authentication factor), which allows more confidence that the thing you have is truly only authenticating you, even if it's in an attackers hands. But either way, you're extending trust and risk beyond the minimum that's required to be most secure.
Of course, your threat model might mean that you judge the risk from having many devices able to authenticate you, potentially all in different places with different people able to physically access the something you are supposed to have, as an unimportant risk. As other comments have pointed out, many 2FA solutions will allow multiple devices. Use your own judgement as to whether the trade-off is acceptable for you.