As many have said, 'it depends'. In my experience the American carriers have less room and more people taking too many/too large carry on pieces. In Europe and Asia I am often on full flights with the bins only half full.
However, I have also see UA almost every week deny people from boarding with their too large/too many carry on pieces. Even here we see people who don't seem to think that they should be subjected to the rules. If a handful of people on every flight think that the rules don't apply to them, then the bins get full very quickly. Remember too that with reduced capacity, there are far more full flights these days.
Enforcement of the rules is finally happening in America; on many carriers at many airports before security, before boarding, and during boarding passengers are being sent away to check their too large/too many pieces.
As to boarding order, it is not back to front. Every carrier varies; for instance on UA it is
- UGS/1K
- 1P/*G
- zone 1
- zone 2 and families with small children
- zone 3
- zone 4
Zone 1-4 is determined by WILMA - window, middle, aisle. Many carriers no longer preboard families with children as it slows down the boarding process.
Sadly, those of us who sit on planes every week DON'T want to have to board first, but we often do just to secure overhead space. I fly bulkhead and must put up all my items. And I only carry two very small pieces so don't even use 1/2 of my allotted allowance on US carriers.