They could, but there are a few good reasons for them not to. First, would be the extra work load and exposure. If they're appearing on both shows, then multiple sets of contenders are after their titles every week. And that can be great in the short term, but it makes it hard to focus on one feud without making the other show feel like it's being ignored by the champion. Personally, I enjoyed having multiple tag titles, back in the day. Both sets of championships felt important, and the multiple titles to compete for actually helped the division grow.
The Women's championship is harder. While we say the tag division looks thin, it's really because certain teams have yet to step up to the plate. Time will tell there. The women's division on the other hand, is far more sparce with believable contenders. I would rather see the ladies land on Raw where they can utilize that extra hour, rather than split the division up. I'm not sure how much good it will do to just have the champ on both shows.