I think it's great to have at least two matches every week (three is even better, but that might be too many for a lot of people).
Given the vagaries of Scottish weather, especially in winter, I think that there's now an even better argument for a 2-month (yes, 2-months) break during the winter.
Start the domestic season in late July/early August. Two matches every week, whatever the competition (cup or league) three when necessary! This should continue until late Nov/Dec, then stop completely until mid/late Feb, then resume again with two/three games per week.
Fewer postponements due to frozen pitches, fewer (maybe not many) truly horrible freezing rain and howling winds spoiling the games, more time for seriously injured players to recover, money saved for fans (and clubs) during the expensive festivities at the end of the year, fewer late postponements that affect hospitality and sponsorship, etc. and interest kept going all the way through every one of those weeks when football is getting played.
Full-time and part-time teams can both handle this kind of schedule, as they are doing right now.