We were on a very similar connection with LH (TXL-FRA-MRU on LH with 1:20 transfer time in FRA and two small kids in tow) when we used the service in February. IMHO it was absolutely worth the money:

The very friendly FRA employee picked us up at the arrival gate, helped us with the luggage and escorted us to the car waiting downstairs (brand new BMW X5). The only stop on the way to the departure gate was a (completely empty) passport control - we drove there, took the lift up, went through, and took the lift back down to the car. Note that since she picked us up at the A departure gate and drove us directly to the C departure gate, we were also spared the extra security check that we normally would have had to do between A and C.

Overall, a very smooth experience, in particular when you have to drag along two small kids and their car seats (to be used on board).