One word -- money.
The restriction on play ups all started when some schools (think St. John's in NYC) only had a D1 team in basketball. When the huge TV contracts started coming in for March Madness, the full fledged D1 schools did not want to share the money with what they perceived as cherry pickers.
So, the initial restrictions started for some sports. Then, even though many other sports are not big money sports, the big D1 powers in those sports also did not want to see certain schools cherry pick their championships. Plus, the big D1 powers felt that schools like Clarkson can put all their monetary effort behind hockey (or whatever that one sport a particular school is playing up) because Clarkson would not have to spend a lot on the rest of their sports being they were all D3. Thus, there was a perception of unfairness. Therefore, all sports restricted themselves to only schools that were going to make a commitment to the appropriate division in all sports, grandfathering those who were already doing so. And in some ways, you can see their point. You want to compete in D1 or D2? Then make the full commitment.
Remember, the NCAA's job is not to care about one sport. It's to care about their entire membership. And it is that membership which votes on the policies enacted by the NCAA. The NCAA is just a governing body. Nothing more. It's the members who decide what the rules are.