This rather economic recycling allows a living cell to absorb damage that would be catastrophic when you just assume that everything works forever just as you imagined. I don't have a guess how much more energy would be expended in reassembly of diamondoids, @titotal@awful.systems might have an estimate, but i guess it's some 1-2 orders of magnitude more. Disassembling and assembling everything at random would be most likely prohibitively expensive in terms of energy, and detecting fault could be very easily hard to impossible. (There are some pathways that are responsible for shredding misfolded proteins, again, you can't do this with stiff things)

Somebody in the comments made a point about how they're sure that you can make something like a protein but held entirely by covalent bonds - while possible in principle, i find notion of such thing absurd and detrimental to fitness - you can't easily make or hydrolyse such densely, permanently crosslinked protein in usual ways, it would require special proteases. Even some cyclic peptides resist digestion, that's because normal proteases turn proteins into unfolded string of aminoacids first and chop it one by one. You can't do this when there's no end. This gets much worse when it's an entire 3d mesh of mess that you can't even move, and there's already an actual biological problem with this - it's linked to nonspecific reaction of glucose with proteins, most commonly, tying permanently lysine and arginine side chains. These are quite appropriately abbreviated as AGEs https://en.wikipedia.org/wiki/Advanced_glycation_end-product

Well, partially, IIUC, because calcium atoms are heavier than carbon atoms. So even if per-bond the ionic forces are strong, some of that is lost in the price you pay for including heavier atoms whose nuclei have more protons that are able to exert the stronger electrical forces making up that stronger bond.

This is so fucking wrong i had to quote this. I don't even know where to begin, calcium atoms have charge +2 in hydroxyapatite and pretty much in any other non-pathological edge case. The bigger (heavier) you make an atom, the less surface charge becomes, this is a bad thing if you want strong ionic bonds

But then, why don't diamond bones exist already? Not just for the added strength; why make the organism look for calcium and phosphorus instead of just carbon?

Because it's already here and making diamond bones is both pointless and prohibitively energy expensive. I guarantee there would be enzymes running on lanthanides, were these more common in, say, seawater

Ionic bond is not really a bond in some senses of this word. It's better to say ionic interaction - bond in some meanings has defined shape, that is there is a geometry that obtains minimum energy. This works in salt crystal, where any disturbance of ion position has to happen along sharp energy gradients. It doesn't really mean anything in proteins, where charges are fuzzier, further apart, and there's water around blanketing every charge and shielding it from others. Here, there might be some things that are attached directly to hydroxyapatite crystal by ionic interactions, I expect some phosphorylated proteins, but don't quote me on that

I don't even think we have much of a reason to believe that it'd be physically (rather than informationally) difficult to have a set of enzymes that synthesize diamond.

Yeah, I'm pretty sure that would be rather pretty fucking hard, especially when you don't have things like palladium or platinum. Making C-C bonds in controlled way is hard enough, making them in regular lattice without any functional groups nearby makes it significantly worse