Here's how I use take-off not before restrictions:
The traffic prediction shows that a sector or group of them is running close to capacity. based upon flight plan data, there is a peak of traffic in one 15-minute period which would push the sector over capacity. However, the overall volume for a longer period is manageable. If I can identify a small number of flights which are flight planned to be in the 15-minute peak and which can be moved back by (often) as little as 5 minutes on their (unregulated) take-off time by placing a 'take-off not before' restriction on them to smooth out the peak, then this seems the best option for all rather than a blanket slot restriction. Don't forget that this is all based upon flight plan times and we don't know when exactly you will get airborne. By ensuring that the take off is not before a certain time we can ensure that you will arrive in the sector after the peak. From an ATC point of view, surely this gives the Tower controller the flexibility to plan and manage their traffic without it being restricted to CTOTs.
As you asy, there is no point in sending a Ready message, as the flight is not subject to a CTOT.
Of course, that means some forethought on the part of tower controllers in starting and taxying aircraft, and another thread on this forum suggests that this is not Jersey's strong point!..