According to the coastguard quoted in the Dorset Echo 'The consequences could have been dire'
There must be more to the story (I hope) because on the facts laid out so far I would seriously question calling out the RNLI fo an expired auxillary enging and a rope that could be cut.
If the story is as written and there is no more to it I hope the RNLI charge well for this 'rescue' and salvage.
We don't know enough detail. If the rope had fouled the prop & rudder, failing to make headway in deteriorating conditions, child on board, etc. then it could well have been justified.