@bewilderedmom,I would describe slots just a bit differently. Rather than “to give kids a chance who may not shine as bright as others in a regular admission pool,” I would describe the purpose as getting highly skilled athletes to attend the school that would not be admitted without their athletic prowess. I think we are saying the same thing. You just have a nicer way of describing it.
Walk-ons are another interesting topic. It depends entirely on the school and the sport, as you have noted. Even at D3 schools that have open tryouts, I don’t think the chances for a non-recruited athlete are great. For a number of reasons, if a recruit and a walk-on are equal, the coach will go with the recruit. Others will know way more about swimming recruiting than me, but I suspect that a sport like swimming the facilities for which have natural size limitations (you only have so many lanes for practice) are less likely to welcome walk-ons than for example a soccer team at a NESCAC school that also has a B team. Either way, if you can get being recruited, it is far better than relying on open team tryouts.