I dunno TEF, you said it looks clear but theres at least 6 different motives that I can think off. She fought like a sissy with no heart, so if she was really fighting Jack she was obviously doing it for someone else and put no effort into it as she wants Jack to succeed.
Then theres 'its was a test' approach, where she would see if she could make Jack rest and divert him from his mission. The smirk at the end could be her happy that pretty much nothing would stop him from getting Aku. Don't usually fight with someone half assed then run away and give an evil smirk if there isn't an alternative motive.
Then again she could have just been out to get Jack for whatever reason and wanted to keep him there for all time so he died and when that tatics failed she fought him but she knew her battle skills where weak and knew it would end badly for her, so she was smart.
Also when Jack was in her arms, the flashes of Aku..was he sensing something from the Goddess of Springs magic or was it just guilt or having Aku on the mind that spawned the flashes.
"or she was simply a very lonely goddess who wanted a companion" Another valid reason, make that 7 different reasons, but I doubt she was lonley in the general way, maybe lonley because she has very high standards and wanted someone as 'pure' as Jack.