Short answer -Yes spikes harm palms.
Long answer-
Wounds in palms are different in that they are monocotyledons and therefore have scattered vascular bundles, so a spike wound may not progress anywhere from localized dieback/drying at the immediate site, BUT could be an entry point for some of the nasty fungi. Any palm wound will NOT callus over, palms don't have that mechanism, all they do is dry out leaving dings and hollows and scars. In high wind areas I can't help but think that an accumulation of spike wounds would lead to a weak point for failure in high winds - hurricanes.
I have spiked a couple of palms as a last resort, hated to do it but it was the only option at the time...I usually use a ladder or a bucket or my 21' hayuchi.
I have seen pictures of palms spiked over and over, and although they are surviving 20+ years they look NASTY!!!
You mention "the bark in growth rings is quite thick'
Palms do not have bark as we know it like dicots, just a secondary thickening, the 'growth rings' are the scars from the attachment of leaf bases, that have since fallen off.
As someone mentioned pruning palms from below, spiking , or even using a ladder (while tied in around the stem) to access the 'petticoat' type palms is very dangerous. The many layers of accumulated fronds are dry, filled with dust, dirt, roaches, rats and other nasties. Also the lower layers are hanging on by a thread, and once you start pulling them off, the whole lot can collapse on you.
Do a search on the threads here, palms have been discussed quite often. Some of the palm guys use a SRT access, throw a line over the crown, tie it off and ascend SRT to the top, then work the palm from the top.
Beware of the Phoenix genus palms, they have NASTY thorns at the base of the petiole that can stab you badly, I've had several 2"+ thorns surgically removed from my arms, one just missed all the vitals in my elbow joint, nearly was a through and through, had disappeared from sight!
In Spain, you should come across the 'tree bicycle' a piece of equipment designed to ascend smooth trunked palms without harming the trunk. There was mention of them in the ISA magazine recently I think...
Happy climbing, stay safe.