I can speak only to my personal experience on this. It was always the large publishers that wanted all the rights. I never had that problem with a small publisher, who you would think would want all the rights and who would maybe make that demand even more strongly than the larger publishers would. That, to me, was always an interesting paradox, because the people who, as you say, had all the power wanted even more power, and the struggling publishers, who were maybe putting out one or two magazines, paid me reprint rights. They paid me if they wanted to put something on their website, and that kind of thing.
Where the solution lies is that there is a balance that can be achieved. It's a question of will and whether the publishers really want to have that. If you can look at it as that without strong content they will not be able to sell their advertising, then they need to pay for that content.