If ever a bird was designed by committee, then this is it.
Anyway, for the past four winters, a male great spotted woodpecker (dendrocopos major) has visited our garden to freeload on one of the hanging peanut feeders contained therein. It may or may not be the same bird. Their lifespan can be ten years plus. (The bird(s) can’t be knowingly allergic to peanuts because I nailed a sign on the fence nearby which states Warning: may contain peanuts). In addition to said hanging peanut feeders, I spread around some loose peanuts, peanut granules, and raisins, foods that cater for the needs of most other birds visiting the garden.
According to this British Ornothilogical Trust 2006 survey (PDF), the supplementary diet of a GSW can include fats, sunflower hearts, bread, biscuits, waffles, chips, peanut butter, and suet. Most of these foodstuffs will not be contained in wire mesh feeders.
I’m curious to know why my GSW always takes the difficult option by pecking for small pieces of peanut from a feeder rather than the easy option of loose available food scattered about the garden.
Being a woodpecker, his idea of how to get a meal is to probe for and dislodge tasty edible nuggets with his bill. Loose bits on the ground don’t fit in with his feeding scheme, and thus have low interest for him.
For an analogy, you probably strongly prefer to eat restaurant food by sitting down at a table and having the food brought to you on plates. Considerable nutrition might be available out back in the restaurant’s rubbish skip but - even setting aside health considerations - that doesn’t fit with your habits and so you probably don’t consider it.
Both you and the woodpecker might behave differently if starving.
The North American “designed-by-committee” bird is probably the Northern Flicker. Note the yellow under-wing and under-tail. The males also have black “moustaches”.
As Xema has said, it’s because pecking at a vertical surface fits with his normal foraging behavior, while hopping on the ground does not. The fact that he will be more vulnerable to cats and other ground predators probably has something to do with it as well.
The BTO survey was carried out in the summer months when natural food is normally freely available. Therefore it is unlikely the GSWs noted feeding on the supplementary foods listed in the OP were in any way starving. I am aware that people sometimes cram suet and bread into tree trunks in order to attract the bird but I am also assuming that not all the people surveyed did this. I am guessing that some foods were placed in a non-peckable location, yet the GSWs still took them.