I guess there are two problems it causes that you might want to solve: the annoyance of the extra ceremony and the risk of losing access because you lose the ke

I guess there are two problems it causes that you might want to solve: the annoyance of the extra ceremony and the risk of losing access because you lose the key. If you don't need more security on top of your existing (presumably high entropy) password, the latter problem might be solved by publishing the totp key. The GitHub bio box is public, mostly pointless and a sensible size... The former might be solved with a bookmarklet that embeds the key and fills out the relevant form automatically. If you're going to publish the key, presumably publishing this in as convenient a form as possible also makes sense.