We are doing this right now and then taking out some kind of mortgage at the end. I don't see any downside.

The downside for us is that at the end it's not a traditional 1st mortgage. The home would have been bought and paid for, so the loan at the end would be a home equity loan, and carry a higher interest rate. I suspect it would take some number crunching on an individual basis to determine the best course. This is info from our bank.

couldn't you do a one-time close with a bank, then at the very end submit a single draw for the entire amount you want to have for your mortgage? This would be cheaper than the home equity route...

If you can pay for it up front, why bother with a mortgage later?

One reason would be if you were earning more on your invested money than you were paying in mortgage interest. There's also value in the security of a paid for house. The answer, I expect, will be different for each family, and even differ in varying stages of life.

That's kind of what we would like to do,might only be 30-50 thousand short.
What would be the best type of loan to use,paying that back would only take a few years?

We did it with a home equity line of credit on the old house which we then transferred to the new house when it was complete and paid off once we sold the old house.