Like tennis or golf, where there are plenty of tournaments every year. The pros: The best will generally meet the best more regularly. Having structure and routine means general sports fans will know when to tune in for the most prestigious events, potentially building up a larger fanbase for the sport as a whole. The cons: Boxers wouldn't need to sell fights, so the majority of them would end up becoming drones with no charisma like in tennis and golf. The fights would probably need to be made shorter, particularly if you were going to have more than one tournament a year. You might lose some flexibility in making great fights, and the best of each division might lose incentive to challenge themselves across different weights, meaning you could actually end up with less great fights.
What you suggest already kind of exists in the form of amateur boxing, and the WSB in particular. But it doesn't seem to attract to many viewers or top level fighters. I think the scarcity and the build up of the big fights is part of the pro game, but I really like the concept of WBSS. So it's hard. I think the biggest improvement of the sport would be if the governing bodies became stricter with their ranking and enforcing of mandatory, both for the champions and the contenders. The champion should never fight someone outside the top 10-15 and they should be harder about who they rank. Unfortunatly I think corruption is to deep in the sport, on all levels, to make that happen. That is the main problem that should be adressed in order to make the sport more popular.
It would definitely help build the sport if there was a more regular schedule and perhaps major events to build towards. If there was a unified ranking system that used a point system like tennis and then that ranking system was used for the top 8 fighters in each division to face off in a series of eliminators with the winner being crowned the champion of that year much like the WBSS. Perhaps it doesn't have to be every year for every division. Maybe every 4 years for each division but each year it happens for a few divisions, the following year it happens to a few others and so on, so in that 4 year cycle all the divisions get a unified champion. It would make the sport far more competitive and fan friendly as means fighters couldn't just sit on a ranking hoping to get a title shot or milk a title by cherry picking weak opposition all the time as once every 4 years they'd be forced to unify all the belts. The regular schedule would make it far easier for fans to tune in for certain fights. Promoting would be made easier, it would be like the Olympics or World championships for boxing. Everyone knows there's these huge events like Grandslams in tennis every year on set dates for a few divisions. Just like most tennis fans tune in for the 4 big Grandslams boxing fans would tune in for these boxing Grandslams. There would be 3 a year, the first round, semi's and the finals. There would be matched from 3-4 divisions so these would be the best of the best facing off 3 times a year in these divisions. They would be very lucrative events where the big money is made. But with the way boxing is, with every promoter, sanctioning body etc looking out for their own self interests it would make it impossible to implement. Every sanctioning body and promoter would need to be involved and honestly I can't see it ever happening unless someone comes into the sport and just drops and huge amount of cash to bring everyone together and we'd be talking billions. Also as we've seen with WBSS things like injuries would make it difficult to organise and remain on schedule.
