The importance of the morning test is debatable. I still do mine, but it is more from habit than anything else. There are too many things that can influence it, most of which are a mystery and outside our control. If you want to see what your normal base-line level is, the best time to test is before evening meal providing you haven't been snacking.
The HbA1c is a reasonable test for diagnosis purposes, and in people with standard red blood cells it is useful to see how much control you have generally. Not everyone has standard red blood cells. (I don't) What it does not do is catch the post meal spikes that cause the damage.
What is important are the post meal spikes. This is why it is advisable to test after meals to gauge what sort of control you have.