Apart from the questions of whether students "should" have experience and whether particular schools
do or don't require it, another concern is how informed you are about your professional goals at the point of being a new grad.
Most people aren't even aware of what a wide, varied
range of career and role possibilities is available within nursing until they've been in it for a while. Many, many
nurses have had the experience of entering or finishing nursing school
with the idea that they are sure they want to specialize in a particular area (often based on personal experiences and/or clinical experiences in school (which are necessarily quite limited)), only to find, a few years down the road, that they're much more interested in something else entirely and are more interested in some role or career path they didn't know existed before.
graduate degree in nursing is going to cost you a lot of time, effort, and $$$ -- I think it's smart to invest a little time and effort "up front" to make sure you're getting a degree that is going to get you where you want to go (for the longer