Interesting. What are the advantages?
A perfect pirouette finishes exactly in handstand. In a straight body cast, the pirouette can be initiated on the way up, which means the gymnast can finish turning at vertical without breaking the flow of the routine. In a straddle cast, the gymnast cannot pirouette until she is already in the handstand; therefore she has to hit handstand, stay there as she turns, and then continue on.
In theory, it should be very slightly easier to consistently finish the pirouette in handstand if it is initiated on the way up, and therefore very slightly easier to connect directly into another skill (this is particularly true for an in-bar skill such as a stalder or toe-on).
Aesthetically, there's some real visual appeal to a pirouette that completes right as the gymnast hits handstand (For example, check out Rebecca Bross's pirouette at 0:50 in
this video). She hits a full handstand at the end of the pirouette without ever stopping (or even noticeably slowing) the swinging rhythm of the routine. For comparison, take a look at Nastia's pirouette at 1:18 in
this video (she does it out of a straight cast, but the timing of the pirouette matches the timing that ANY pirouette out of a straddle cast will have). Notice how she goes up, stops, and then pirouettes; it simply doesn't look as nice as Bross's pirouette through handstand without stopping, in my opinion.
In practice, however, the advantages of the early pirouette are almost negligible. Most gymnasts -- even at the Olympic level -- don't bother connecting in-bar skills directly out of pirouettes. Few observers will notice the difference in rhythm between a pirouette on the way up and a pirouette in handstand, and even fewer (even among judges) will care. And while it may be easier to finish an early pirouette in handstand, it's REALLY hard to start the pirouette on the way up, even for gymnasts who can already do a straight body cast.