I played with rogue Hawke, then Bethany had become Warden. I do not see reason that Hawke why left at home his/her mage sister. If Bethany at his/her side, s/he can take care of her. In the Deep Roads relatively few Templar lives, therefore it safer place for an apostate, than Kirkwall ... Do not forget: you can already see in Act1 too, that the Circle is anything but not safe.
That's ignoring how insanely dangerous the Deep Roads are to non-Wardens. Bethany isn't a dwarf or physically enhanced in any way, doesn't wear armor and she signs on as a bodyguard, nobody else aside from Merril make themselves that vulnerable to the Taint. Anyone who cared about her well-being and didn't consider the party immortal could have predicted that she would be the most likely to catch darkspawn sickness, and dragging your little sister along to face risks like that is pretty damn reckless.
"I can protect her better in the Deep Roads" isn't a realistic thought, a Hawke who is protective of Bethany has to be entirely aware of all the ways s/he can't protect Bethany in the heat of battle or on a long march through a hyper-infectious environment, just like s/he lost Carver to the ogre. It's a choice between dragging Bethany into certain and sustained danger or leaving her in the uncertain danger of having to lay low for a few weeks. And unlike Carver, Bethany herself is mostly just interested in going because her brother/sister is, and is almost relieved at being left behind.
And in the end, Bethany is much happier as a circle mage than she is as a Grey Warden. And I can't blame her, the Wardens suck ass as an order.
Bethany barely feels like a character to me. She only exists to be the little sister that needs to be protected at all times.
And Carver is just the little brother who needs to be reigned in and constantly has hissy fits. Wow, what character. At least Bethany has actual opinions and family relationships more complex than "daddy loved my sisters more, my sisters are more awesome than me, I wants tuu be sumwun twooo!! >.<"