There are quite a few problems with quotas for Yosemite as a whole. First of all, they are inherently unfair. Remember that crowding at Yosemite is less a Yosemite problem than a Yosemite Valley problem. It is unfair to punish someone who wants to hike to, say, Parker Pass with a strict quota just because the Mist Trail resembles a New York City sidewalk.
Another problem with quotas is that they tend to favor unsafe behavior. For instance, it has been documented that, as a percentage of visitors, Half Dome quotas have made Half Dome MORE dangerous rather than less. The problem here is that quotas encourage people to hike when they probably shouldn’t. For instance, people are less inclined to turn around in bad weather if they know they can’t just come back next week. Similarly, someone might just go ahead and climb Half Dome with an overuse injury that would probably be 100% better with a couple of weeks more rest. The bottom line? Scarcity of opportunity causes people to not want to give up their chance to hike, regardless of the risks.
Finally, a quota for Yosemite would erode public support for Yosemite National Park, and national parks as a whole. Remember that a BIG part of people’s love for national parks is the idea that they are something that belongs to everyone in the country and can be visited at any time. When people KNOW that they can’t just visit their parks when they want, they don’t want their tax dollars going to support it. This is not such a problem for such things as Whitney and Half Dome (which relatively few people hike compared to the population at large). But if you start putting limits on visitorship of the park as a whole, people will cease to see Yosemite as something worth supporting.