Just a few thoughts:
Presumably, people are less likely to spend as much time in their closets as in a kitchen or office, so they probably wouldn't use the full suite of Show capabilities there as much.
The scale of the Show is probably too large to look good on a small dressing table or side table; whereas space may be at less of a premium in the kitchen, living room, or office.
The Look is a much prettier / cleaner / more modern design, which fits better in the intended use case of a "style assistant" - you have to associate style help with someone whose own sense of style is good.
Look is much cheaper to manufacture: missing the big screen and the relatively large speakers (and the amplification circuitry to drive them).
If you needed one device to satisfy both use cases as well as they each do their own, you'd have to have all the cameras of the Look plus the screen and speakers, etc., of the Show, meaning the price would probably end up more like $299, which is a big difference in the world of consumer electronics.
Amazon likes team to have independence and ownership of their own roadmaps and destinies. If the Look team is closely aligned with the Apparel category and reliant on a bunch of visual processing algorithms, that might be completely different from the Show team's needs and dependence on two-way communications and messaging platforms.