It's actually really important for Wyoming. Right now, Laramie is a designated olympic training center for wrestling. Therefore, student-athletes may attend school and also qualify for an extra "olympic redshirt". Tyler Cox will actually have attended for 6 years before his eligibility is up. If the olympics go away, so too does the designation and unfortunately that would take away a big recruiting tool.
BTW, Wyoming has 3 wrestlers that are ranked by every publication. 2 of them are from Wyoming High Schools (Cox-Gillette and McCulley-Rock Springs). I think Kevin Kessner-Rock Springs was the last Wyoming wrestler from a Wyoming High School to place and become an All-American. I think there is a legitimate shot both McCulley and Cox obtain All-American status at Nationals this year.