Like this you waste charging cycle. I doubt this "few minutes before leaving home" can charge your phone up to 100%. Every cycle you do not charge from 0% up to 100% can be considered a wasted cycle. And in wasting things we are good ;)
That is not accurate, as far as I understand. The opposite might even be the case.
From what I understand, the battery is damaged most when close to 0% or close to 100%.
So, if a phone could do, say, 1000 full cycles until the battery reaches a certain stage of degradation, and now you used an identical phone, but with shorter cycles only down to 20%, then charge to 80%, you could not only do 1000 of those short cycles, but even 1000/60% = 1667, and still have the battery in a better shape than the one with 1000 full cycles.