Yes, witch hazels all bloom on old wood but there is such as dichotomy between the bottom and top of this example that I would make sure the upper part is not all H. virginiana rootstock sprouts before I decided the cultivar was doing this.

I have two witch hazels, both are 'Arnold's Promise'. None do what your 'Diane' is doing. They bloom evenly on the entire shrub and drop their old leaves to the ground. I've seen what you described on shrubs for sale in garden centers and once asked a person working there what's with those old leaves stuck to the plant and obscuring flowers. I was told it is something happening to drought stressed plants, especially in late Summer. I don't know the source of this information but I did in fact water my witch hazels a lot during Summer and did not experience the problems you have with your shrub.
Pick those old leaves and try to keep your plant moist during Summer and see if it makes any difference next Spring.

I'm pretty sure it's root-stock sprouts - I'm looking out the window at a similar thicket coming up from beneath a Chinese witch hazel that has been growing - and suckering from below the graft - for many years here. When these are recognized for what they are and cut off the dead leaves will go with them.

I went to Molbaks today. They have probably around 10 'Diane' witch hazels for sale now, all about 2 feet tall. ALL are blooming only on the bottom half of the shrub but are full of buds along the entire length of twigs. I'm willing to believe that that's the sequence of blooming for these plants, first the bottom half, than the top. No old leaves but I'm sure if there were any they were removed before bringing plants to the retail area.

Sprouts shown in OP have appearance of H. virginiana rootstock. If those are cut off then flowering portion that is left will resemble plants at nurseries.