In the Pro 14 conferences have helped foster new rivalries which weren't there in the past. They've worked extremely well in that competition.
The then Top 16 also employed the conference system until 2004 as a way to keep the number of fixtures down. That system so you play the other team in your pool twice. The top 4 in each conference entered new pools of 4, playing each other twice before semi finals and a final. The bottom 8 played the four teams from the other pool twice each with the weakest teams relegated.
https://en.wikipedia.org/wiki/2003–04_Top_16_season
Whether they'd work in the Premiership, I have no idea.
As a Munster fan who would watch a lot of games in the PRO14, I do miss the old format a little, especially with Leinster in the other conference. Miss the battle between us, Leinster, Ulster, Ospreys, Scarlets & Glasgow at the top of the table. All fighting for four spots. Two home quarters for grabs plus bragging rights. With the likes of Cardiff, Edinburgh & Connacht sometimes causing upsets up there. In Connacht case actually winning it a few years back.
It was very very competitive. It's s little bit more dull now. Leinster are running away with there conference with probably the two teams who would be most likely to challenge them, ourselfs & Glasgow, fighting out amongst ourselfs in the other conference.
I think the big thing that's happened with the expansion of the SA sides, isn't necessarily the introduction of conferences or even the quality which they brought, let's face it hasn't been great. But the extra money in regards TV rights. As we are some bit behind the Premiership and especially the Top14 in that regard.
I think the conferences though will be short term. Hopefully. We are looking to expand up to 16 teams, which seems to be the magic number apparently for numbers. If/When that happens, I say it will be moved back to a single league. With 15 games or 18 games including derbies, home & away. Better everyone plays once IMO, as it would be fairer. Could have a seperate competition for derbies, league counting doubly, plus a PRO 14 Cup, for younger fringe players during internationals and to make up for the lost games.
Regardless, the point of this almighty speil, conferences are a bit of a means to an end. We've adopted them as really no other system would work logistically. They've destroyed Super Rugby. Reality is the Premiership is quite lucky to have divisions. Allows smaller clubs to grow more naturally. Borders went bust a number of years back because they couldn't keep up with the Jones's. I'd only be delighted if one day the PRO14 gets the opportunity for a second tier. Too many regions across Scotland, Wales, Italy without representation. That can't naturally grow.
The problem from what I can see from the outside looking in with the Premiership at the moment is gross breach of the wage cap. Causing clubs to be in serious trouble financially. And now there sh*tting it a bit, causing short term thinking. Until the RFU get that in control and the clubs into a healthy position, they'll continue to be problems, maybe a lot larger ones down the road.