It's not really a glut. Look at when the characters were introduced.
1930s: Bruce Wayne/Batman I
1940s: Dick Grayson/Robin I/Batman III/Nightwing, Selina Kyle/Catwoman
1960s: Barbara Gordon/Batgirl I/Oracle
1980s: Jason Todd/Robin II/Red Hood, Tim Drake/Robin III/Red Robin, Helena Bertinelli/Huntress
1990s: Stephanie Brown/Spoiler/Robin IV/Batgirl III, Cassandra Cain/Batgirl II/Black Bat/Orphan
2000s: Kate Kane/Batwoman, Damian Wayne/Robin V, Luke Fox/Batwing
2010s: Duke Thomas/Signal
Very gradual.