BYU is definitely the best education for the price for undergraduate schooling. But if the LDS thing isn't for you, there are other great universities that are much cheaper than Ivy League Schools. Unless my child was able to get a scholarship at an Ivy league school, I would strongly advise them to go to a cheaper university for their undergraduate degree, and then go Ivy League for their masters degree.

3 and 4 are not reasons not to choose BYU because you can get those at BYU just as easily, and even better because BYU alumni are very helpful when looking for job opportunities.