Starting with Lavell in 1972 BYU has seen only 3 coaches at the helm. That is an average of 14 years per coach. That tells me that when you come to coach at BYU you can stay here as (Crowton aside). I would think this loyalty and commitment from the school would be a strength in the next coaching hire in the future. Of course the flip side is that BYU coaches are complacent with the job security.
Wikipedia said that after 1984 Lavell was offered the Lions and U of Texas head coaching jobs, but declined them both.