I wouldn't go anywhere much without my wallet. She drove to school so she might have her wallet/purse if she intended to fill up with petrol, stop off for groceries, in case she broke down and needed her AA card (hypothetical) etc. I think it's odd nothing's been said about missing personal effects (assuming it hasn't - there's been so much information to keep up with), and these are the kinds of things that might have been found in the river even if her body had travelled downstream of the search area, but haven't, which is (well, may be) noteworthy.
Personally, I think when someone goes missing, apparently unexpectedly, the possibility of a crime should remain uppermost even while other avenues are being explored, because the window of opportunity for evidence-gathering begins to close almost immediately.
JMO