It's a great question! Some of my answer will be taken from my answer to your question on the AI stack exchange, but cross-site questions are allowed and your question here is slightly different so my answer is slightly different. I'll address your points in reverse chronological order:
(4) Most proteins don't have metals at all.
It was estimated in 1999 that about 50% of all proteins are metalloproteins, and in 2009 that at least 25% of all proteins are. So quite a lot of proteins are in fact metalloproteins. Maybe not "most" of them, but certainly enough to use as training data for the purposes of what AlphaFold has done so far.
Also it's not exactly the protein itself that has the metal in metalloproteins, since naturally occurring amino acids that we know so far, do not have metals. Instead, the metal is contained in a co-factor, which is separate from the protein but plays an important role nonetheless.
(3) The more complex electron shell of metal atoms also makes the data less useful, since its bonding pattern is more flexible than carbon, etc.
It is true that metals are typically harder to model than C,H,O,N,S, if doing ab initio calculations on the metals or metal-containing complexes. However the purpose of machine learning in protein folding studies, is to skip ab initio, statistical-dynamical and/or molecular-dynamical calculations of the relevant structures and simply use training data to predict the protein structures. Therefore, while solving the many-electron Schroedinger equation typically has a cost that scales exponentially with respect to the number of electrons, it is not true when using a neural network (for example) to "learn" patterns in the solutions to the Schroedinger equation and regurgitate them with cost that scale only linearly.
That being said, there needs to be enough training data available (as you correctly pointed out) to learn what happens near the metal co-factors: The answer to this is that there's indeed enough metalloproteins to sufficiently populate a training set, but they won't always contain enough of the specific metals involved in every metalloprotein. For example lots of data will be available for proteins containing Fe since Fe is in hemoglobin (for example) which is essential to the functioning of red blood cells to absorb oxygen; but the protein vanabins contains vanadium which is much more rare and therefore training data involving it will be much less available. You're also correct that metal elements can form more bonds than typical elements found in organic compounds.
So it depends on the metal in the relevant co-factor. Fe-based co-factors will have quite a lot of training data available, as will Mg-based ones, Zn-based ones, and a lot of other ones which contain the "more common" metals. For proteins like vanabins which contains vanadium, you are quite correct that training data will be limited, but also keep in mind that vanabins is a very rare protein found in sea squirts and we already know more about its structure (through X-ray crystallography, which means we don't need machine learning for it) than we even know about what it even does. The chances of other vanadium-containing co-factors in metalloproteins being very significant is too low to justify working on protein folding algorithms specifically for them.
(2) Typically, there is only one (or a few) metals in a protein, which contains far more other atoms. So, the structural data that could be used to train AlphaFold could contain far less information about the metal elements.
That's true, but molecular dynamics simulations can be done on billions of other systems that contain metal elements (and X-ray crystallography structures, or other experimental structures), to generate training sets that could help with this. Training the neural network to learn about the effects of metals on molecular structure, can be done on plenty of other systems that contain proteins, not just metalloproteins.
Remember though that AlphaFold is for the most part a "proprietary" software written by DeepMind which is owned by a for-profit company, and while there's some information available about AlphaFold, we don't know everything about what went into AlphaFold. I would guess that they didn't actually train their machine learning systems to understand how metals work in the settings of non-proteins. I would guess that this level of sophistication wasn't needed for the CASP13 and CASP14 competitions in which they participated.
(1) Commonly, the metal is at the active site which needs the most prediction precision.
While it's true that "commonly the metal is at the active site" as in hemoglobin's binding site for oxygen, it's not true that the active site is the part that needs the most prediction for protein folding precision: the example again is hemoglobin, where a single substitution of glutamic acid with valine (far from the active site) completely changes the shape of the protein to the extent that people with this mutation are said to have a disease called "sickle cell anemia". Nevertheless, that is testament to the fact that minor changes in anything (including the presence of a metal-containing co-factor), can cause huge changes to the overall structure, which is probably why such complicated quaternary structures are not likely to be present in CASP competitions just yet (but let's allow someone working more closely in that domain, to answer in better detail about this part).
