Devils Advocate
That's exactly what 2 Six 4 is saying and he/she's right.
The individual ACCs advise the CFMU of their sector capacities, firstly on a strategic basis (i.e Ops Normal) and secondly whenever conditions require a different capacity to exist. It is these figures which are fed into the Wurlizter and are used to calculate globaly whether you are restricted or not.
If you are given a slot, it will always be possible for your company (and the CFMU) to find out which sector is causing the most penalising delay on your route. If that sector then changes cirumstances and ups it's acceptance rate, then your details can be fed back in and the whole process started again. However, it doesn't mean because your most penalising restriction has been removed that you now get a clear run at things. That's because all the less penalising delays which were 'hiding' behind the biggest one now come into play. They are still there and have to be taken into account.
The CFMU have no say over the capacity an ACC sets and no influence on the guys at the coal face. As they have only a sparse knowledge of the airspace and no knowledge of the ATC procedures and staff levels and capabilities at the ACCs, there is no way that they could.
I am not sure if any non UK ACCs make use of it, but in the UK we do have constantly updated information from the CFMU on the pain that the UK is causing (using the CASA Delay Monitor). This will flag up aircraft in the system where 15 minutes or more delay is being imposed with the most penalising delay being due to a UK sector. This gives us a trigger to take a look at individual flights to see if we can do anything for them. For example, we may suggest to the operator that he refiles below the restricted sector, or if it's UK interenal flight, we may speak to the adjacent UK ACC to see if it can take an extra flight over and above the regulated capacity. Of course this is not quite so straightforward if the flight is going beyond UK airspace since although we remove the UK penalty, the CFMU then has to recalculate all the other restrictions through which the flight will have to pass. Your 1 hour delay in the UK might still turn out to be 58 minutes if that's what Paris are regulating. It's just that the Paris restriction was 'hidden' behind the UK one before !!