If over a period of two weeks a regular important routine is followed. It
would be nice to be able to distinguish those days differently, just by the
background colour, from the non-routine days.

Example!

A person, A, is divorced and gets their kids for 6 days every 2 weeks, the
other parent, B, gets them for 8 days. The pattern repeats. A gets kids on
Friday and returns them the next Thursday, B gets them Thursday and gives
them back on the Friday. And so on.

By simply seeing the differently background-coloured days it would make
planning holidays, checking weekend free-time, much easier...

I am sure this can be applied to many other situations, for instance people
on shift patterns, etc.