Well maj 6th are ok is some context to me. I kinda like it on the IV chord in a I IV V chord progression in a major key. I guess you can say in a cheesy chord progression as such, a cheesy chord is suitable. ;) As for a tonic chord being a maj 6th, that's questionable. The hint of minor makes it an inconclusive tonic. And for a laugh in bad chord analysis, I always see this spelling on the first 2 chords. Cmaj6 - Am7. 'LOL' (later chords may justify this but it usually doesn't)

As for minor 6th, those are cool. And yes they can be seen as a possible sub for a dominant chord, but it's not wrong to not think of it as such. All personal choice here.