I'm okay with the qualifying system as it exists... I think it matches up operational requirements of the tournament with the goal of correctly sorting the teams. Its not perfect, of course, but it is as good as a round-robin is likely to get.
Round robin tournaments aren't the only way to organize a tournament however. I think a
Swiss System type tournament could be organized where all the teams start at the same level, but either advance or drop down based on their record.
This way, while teams play their first match in random alliances, it would quickly work out so that top teams ended up playing against/with other top teams, while weaker teams would play against/with other weak teams.
It would take some planning, and I'm certainly not saying that change is needed... I'm just pointing out that change is possible.
Jason