That’s how it used to be, and, as i recall, the hunter community begged for a long time to get selectable pet specs back.
But Blizzard has adamantly refused for specious reasons, and at some point we just gave up begging for it.
Apparently using using the same one or two pets for everything makes pet families more “unique” (which in this case, for some odd reason translates to “never used”) and improves “immersion” (which in this case, for some odd reason translates to “never feeling motivated to tame new pets”).