Ice and water shield
 

Would it be a good idea to use ice and water shield on an entire roof and not use felt or synthetic underlayment? I can't see any reason not to other than in 20 years, it'll be a crappy job to strip the roof.

If the roof isnt a low slope then I wouldn't. Cost alone would be my determining factor as it wouldn't add any benefit since snow n water wouldn't be sitting on it potentially causing damage. Just my thoughts as if you want to spend the $$ and are able to go for it.

Ice n water shield in most commonly used under a metal roof that has been insulated on the exterior. It acts as a air barrier as well and seals any screw penetrations. Waste of time and money if installed under shingles.

It is used in the first row and in valleys or around skylights and chimneys only because those are the only places where you can have potential snow and water buildup that creep back up under the shingles. Using it anywhere else is just overkill and has no added benefit.

If you want the best value out of your roof spend extra on venting. If an older home open up some soffit venting to supplement the roof vents. If your roof isn't properly vented your shingles will not last their rated life and ice damming is a problem. No roofer is going to bother because it is time consuming when dealing with proper venting.