Calendars are short gamma and long ve. So you want vols to rise absent movement, unless they are traded OTM, and those conditions are generally in opposition. Either trade them LVLD or tethered to spot/futures.
Don't forget "Juneteenth" on the 19th of June And leap years have 366d Where have you been to school, man?
Time as synthetic vol. There are a million use cases. But yeah, timing earnings-releases where the vol-switch inverts. Long CPI vol and short pre event. Street assigns a premium figure to fixed-delta and again, the vol-switch diverges.
This is a naive and simplistic view. The reality is that cals are a little more complex than that. An increase in general market IV normally results in the short IV increasing much more than the long IV. What we want in the cals is not vols to rise, but 1) long vol to rise more than the short vol 2) or short vol to fall more than the long vol We are trading the IV differential between the two.
in your example the vol surface has moved in root time flat (no twist). No net pnl in a 1:1 calendar as the front has less vega than the back. Des is right, because in this event of a root time move, if the realized vol is the same, you "get back" the loss on the front, but keep the gain on the back.
Reading quant books is one thing and actual,real life trading is another. Your post is like a physicist showing differential equations and advanced level maths to a bumble bee, telling it, that according to science, the bee cannot fly, and the bumble bee simply smiles, says "Yeah sure" and wizzes off into the air. There are traders, including myself, who regularly trade calenders during FALLING vol (post-earnings) and closing for a profit cos the short iv has fallen much more than long iv. The root time square vol hexagonal vomma trangulated shadow gamma sticky surface etc doesn't come into the equation cos the trade is closed within minutes. But others can trade cals the way it works for them. To each, his own.