Has ii-I ever been a plagal cadence or is this site incorrect? https://www.simplifyingtheory.com/perfect-imperfect-plagal-deceptive-half-cadence/
The usual definition of a plagal cadence is IV (or iv) moving to I. Put another way it's the subdominant chord (IV or iv) moving to the tonic (I). (See references below.)
The website takes a looser definition. Rather than specifically referring to a (the) subdominant chord, it allows for a subdominant function chord, which can be a ii chord. Of the sources I consulted, none includes this more permissive definition.
Although inconsistent with more standard sources, there is a bit of wiggle room. Aldwell and Schachter (see below) allow for a "sort of" ii chord to participate in a plagal cadence.
As we saw in the excerpt ..., the apparent 6-5 [chord] occurs where a 6th is added to a 5-3 chord. This happens most often with IV.... In such cases the "II[6-5]" [i.e., ii(6-5)] is really a IV with added 6th. Such IV chord occur frequently at plagal cadences. (p. 390-91)
Thus, where the website allows that ii7-I is a plagal cadence, Aldwell and Schachter would say this is primarily true when the ii7 chord is in first inversion — ii[6-5] – and that it's not really a ii chord at all, but a IV chord with added 6th in disguise.
The progression IV-I, used as a cadential formula, is called a plagal cadence.
Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. (Harcourt Brace Jovanovich, 1989), p. 182, emphasis original.
The two-chord motion IV-I is called a plagal cadence.
Steven Laitz, The Complete Musician, 2nd ed. (Oxford University Press, 2008), p. 336, emphasis original.
A cadence consisting of a subdominant chord followed by a tonic chord (IV-I).
Stanley Sadie, ed., The Norton/Grove Concise Encyclopedia of Music, rev. ed. (W. W. Norton & Co., 1994), "Plagal Cadence", p. 625.
A cadence is normally called 'plagal' if it consists of a tonic chord preceded by a subdominant chord (Ex. 11). [The example referenced illustrates IV-I only.]
Alison Latham, The Oxford Companion to Music (Oxford University Press, 2003), p. 193.
Plagal gets its name from the way your ear expects it to go to V but it ends up going to I. This chord is also called the Amen chord because it is how much of traditional church music ends. IV - I works because both chords have the tonic note which means one of the voices can rest during the cadence. II - I has the notes 1-3-5 AND 2-4-6. This is a pattern that is very hard to harmonise to a satisfying degree. These notes are just going to clash.
The important part to note about cadences is that they are musical full stops. It is the device that we use to end phrases of music. We want the ending to be satisfying and the moment you start substituting chords or messing with inversions then it takes away from that. You have countless ways to make your music interesting but when you want it to end, it just needs to end.