I couldnt agree more I now have an old hand shredder mounted by the compost bin and everything that goes in the compost goes through it first.
This year I have produced the best compost ive ever produced, pesky Brassica stems that never seemed to rot down are now rich black compost in a matter of weeks.
This I am finding is the perfect mulch for my garden. In the past having a few trees that need annual pruning to keep them in line was valuable too as the branches were put straight through the electric mulcher and straight on to the garden, no cost really apart from some labor and the initial cost of the mulcher, which by the way I feel is the best investmesnt ive ever made considering what it cost to dump rubbish at the refuge station.
It was purchased about 25 years ago, it is basicly a hopper with a handle cranked hand mower blade no good for big stuff but works extrmely well on the average grden and kitchen waste ill try and get hold of a camera a put a pic up.
Comfrey is another good thing to grow as it rots down really well as a mulch under trees and gives a mountianous amount of nutrients back to the soil pulled up from the lower areas as the roots penetrate deep.
Just be aware Comfrey can get a little, heck what do i mean - alot, invasive if it allowed to rule the roost.
A layer at the bottom of your potate trench before you plant works wunders in providing the nutrients fora good crop.
pea straw is recommended as it has a very high easily/quickly composted biomass and is generally high in nitrogen, compared with other straw, as it is from a legume. it is a wholeplant straw, rather than a stalks only type.