My proposal would be simple:

• 10 kg checked bag for free on light fares (23 kg for SkyTeam Elites), with no restrictions on size other than usual limits for checked bag.
• Only personal items included on all economy fares, carry-ons at an extra charge higher than the extra checked bag fee.
• Free carry-on for business class, Ultis and maaaaybe Platinum. Gold would already cover too many people.

Then I'd believe it's not just a money grab but an actual attempt to improve the experience The only thing I haven't figured out is how would boarding work in my proposal (where some groups are meant to get priority boarding but not a free bag).