If he had done so, he'd have forced the slimy Michael Howard et al to either come out publicly and stand against him - and be seen by the membership as having been responsible for the mess - or be forced to make the calculation as to whether or not to support who ever was brave enough to stand.
If say David Davies did, Howard would have to hope that Davies got enough votes to topple IDS, but not enough to actually win himself. Tricky!
Now there's going to be a vote of confidence in which they'll both say in public how wonderful IDS is while voting 'no' in private. When - and I'm sure it will be when - IDS loses, they'll stand in the subsequent leadership election saying 'I regret that he lost, but now I am free to stand, I didn't cause this, vote for me.'