For me, the gripe re. the time delay was not having my passport* for an unpredictable length of time - I'd been told they normally took a week to 10 days. I needed mine after passing my PPL, so it was a month before I could send it in, then 3 weeks before it got back. By that time I had to be away again for a few weeks.
My local flying school wouldn't accept the temporary licence as they wanted to see my medical (granted I could have taken a copy, had I thought of it beforehand) before they would rent out an aircraft.
Long and the short, 3 months after doing my skills test, I haven't yet gone solo again. Whilst flights with an instructor are never wasted, especially when flying a new aircraft in a new area, what I really needed was a few hours of solo consolidation and I'm now considerably de-skilled relative to when I passed my PPL.
Now, this is as much due to my lack of foresight and somewhat busy lifestyle as to the CAA, but if they had been upfront about the delay I might have done some things differently.
*Yes, I do realise they'll take a birth certificate if you have one handy.