The women's nationals race was even bigger, with 108 finishers. 53 out of 68 women who finished outside the top 40 were in their second race of the champ (78%), and if 80% of them opted to skip elites due to the age-group-or-elites cutoff then your women's field would have been 66. (46 women started in Austin this year).
The bottom line is that traveling halfway across the country (or more) just to get blown out of the water and pulled off the course isn't something a lot of people want to do. But if they're already at the venue, they'll pay another $75 to race a second time, even if they're not fast enough to have a chance of finishing. Because they love racing cross.
In summary, the elite race would actually self-regulate quite nicely using just the "age-group or elites" criteria, and I think you'd see field sizes in the 60s. Most of the field size reduction between 2014 and 2015 would have happened even without a qualification standard framed around a UCI series that is inaccessible many racers.
Additional hypothesizing for people who really really think Nationals should be a small race:
If for some reason 60-ish starters at Nationals is too many, you could always try making Cat 1 mean something for the first time in cyclocross history, by restricting the race to cat 1 only: this would have excluded 34 men from 2014 Nationals and a whopping 55 women.
(Obviously some of the cat 2s would upgrade, but this would send the "this is a super fast non joke race" message -- I know that I personally would not have tried to get a Cat 1 cx upgrade in 2011 to race Nats)