What you are describing is different from the franchising model operated in the UK. For the most part, the privately-owned train operators (in fact, some of them are owned or part-owned by DB) in the UK have government-granted monopolies on their routes. In general, they don't actually compete with each other like these German private operators do.

So, in the UK you have a model where you have the disadvantages of privatisation - private profits being extracted from the system - without the advantages (i.e.: competition). We have also seen that while private operators receive the rewards of operating successfully and efficiently, they do not bear the risk of failure - such as when National Express was able to walk away from their loss-making East Coast franchise, leaving the government and taxpayer to pick up the pieces.

Under this UK model, I think your concerns about cost are valid: privatisation has not brought savings to the taxpayer in the UK. However, IMO it is for the most part incorrect to describe UK TOCs as providing a "poor quality service". On time performance has improved steadily since 2001, and is now over 93% across all TOCs. Not sure DB provide comparable figures, but I would be surprised if it were significantly better. And this is on a rail network which is significantly "denser" than in Germany: more trains operating on less track. Of course, this has been achieved with significant investment from taxpayers, so private operators can't be given all the credit.

Personally I think the franchise model works well on regional and commuter railways, however the major intercity routes (ECML, WCML, channel tunnel) should be opened to full competition. These are the most profitable routes by far and there's no reason competition on them wouldn't bring innovation, high quality services, and cheaper tickets - while still providing a return for the taxpayer (which in turn can be used to subsidise unprofitable regional routes..)