If a show has something that will draw crowds on the road WITHOUT a Broadway production (it is a revival of a hugely popular classic; it's an adaptation of a beloved source, particularly a family-friendly one; it has stars that are proven box-office draws), it may make sense to tour for a while.
Producers can rake in the cash and pay off most of the cost of mounting the show BEFORE facing New York critics. Those critics can sometimes turn a hit into a bomb virtually overnight.
(Of course, sometimes a pre-Broadway tour is extended while work is done on the show, but now that previews charge full price, this doesn't seem to be as common as it was once.)