As far as I understand, the main reason why an authentic cadence (i.e. V–I) works well and is so common, is that the dominant chord contains the leading tone, which resolves very strongly to the tonic. It also has a common tone shared with the tonic chord. vii°–I also works well as a cadence owing to the resolution of the leading tone. I presume the main reason why it's less common than an authentic cadence is that the diminished chord is dissonant.
But what about other possible cadences with the leading tone resolving to the tonic? The most obvious one is iii–I, which has a leading tone resolution and two common tones. You might think that iii7–I should be fairly common since iii7 contains V. (Could you consider iii7 to be Vadd13, making iii7–I a kind of colourful authentic cadence?) Another possibility would be Imaj7–I. However, I don't know any examples of these chord sequences being used as a cadence. Is there a reason for this?
I've tried them out and, while they don't sound all that cadential on their own, if you stick a IV at the beginning, they all seem to work, especially IV–Imaj7–I (and if you extend it to vi7–V7–IV–Imaj7–I, it sounds even better). Even if the answer is just that they don't sound as good as an authentic cadence, is there a logical reason why they don't sound as good, or is it just because we're more used to hearing more common cadences?