A lot depends on whether you're worried about appearances. A neighbour of mine used to shred the fronds, he had a 5 HP shredder and used to produce big piles of mulch. I don't have a shredder but I sometimes chop up a lot of fronds for use as mulch in the garden. I think it's great, although you can get some nitrogen draw down. If it's palm trunks I treat it the same but place them where they blend in until they rot down. I don't remove any organic matter from my place, it all gets recycled back into the soil. However, gardens on a smaller scale can be aesthetically affected by the presence of bulky materials. But in my view having the organic matter/mulch is important.

If the palms were destroyed because they had ganoderma, you would be spreading the fungus all over your plants.

Hi
I find all parts of palms incredibly slow to decompose .yet they are the largest part of my yard waste lol I keep a large compost area and shear off the leaves but have the
trunks main frond hauled off . Don't like slow decaying matter around due to ants and ternmites I do use some parts for growing epiphytes and they can last for several years . Another part that is troublesome is seeds many palms are sooo prolific not only slow to break down they sprout lol. maybe someone will come up with a good use for them?? gary