Water is not an integral part of the structure of leather
Don't take my word for it. Look it up in "Tanning Chemistry, the Science of Leather" by Arthur Covington, now Emeritus Professor of Leather Technology, University of Northhampton. This is considered the standard leather chemistry textbook. In it he says
An important part of the structure of collagen is the role of water, which is an integral part of the structure of collagen and hence of its chemically modified derivatives.... (Chapt 1, 1.4, p. 10)
The involvement of water in structure is an important feature of collagen, because it influences the relationships between drying and subsequent leather properties. If the drying conditions are severe enough to remove water close to the triple helix, the fibre structure can approach close enough to allow the formation of additional chemical bonds. This adversely affects the strength of the leather by embrittling the fibre structure and the handle or feel of the leather is stiffended.( page 13)
The water in collagen can be divided into three main groups: structural water, bound water, and bulk water. Bulk water has a liquid-like character and can form ice crystals at 0oC. Bound water exhibits a structure between solid and liquid, and does not freeze at 0oC. Structural water molecules are part of the fibre structure and behave like a solid.
In the earliest stage of drying there may be sufficient bulk water on the surface of a leather for it to act like a liquid water surface. Evaporation occurs at a constant rate, which is proportional to the surface area of the leather (A), mass transfer coefficient (Kg) and to the difference between the vapor pressure of the water at the surface temperature (Ps) and the partial pressure of water in the air (Pa). Chap 18, Drying, p.421-422)
Part of the process of converting skin to leather is to modify the collagen structure by replacing the oxygen atoms in the hydrogen bonding with amino acids in the tanning solution
Well, you cannot "replace oxygen atoms with amino acids". Chemistry does not work that way. Amino acids contain oxygen atoms. Oxygen atoms are much smaller than amino acids, and amino acids would not fit into the locations where oxygen atoms are found in the amino acid chains of collagen- or for that matter, any other protein. To the extent that hydrogen bonds are formed then they would have to be with atoms like oxygen. Since the proteins are made of amino acids, the hydrogen bonds are between hydrogen atoms and oxygen or nitrogen. So, if you "replaced" an oxygen atom with an amino acid, you would have replaced it with a molecule that contained oxygen and nitrogen, and hydrogen bonds would still form. But you could not do this because the protein structure would not permit it.
Fats are not permanently bound to leather;
Yes they are as part of modern leather fat liquoring. This is part of the reason that leather loses little fat during its lifetime. The methods used to fat liquor involve carefully controlled temperature, ionic strength, pH, emulsification, and agitation- chemistry again. The fats then bind to the leather and stay there. You might see "Theory and Practice of Fat Liquoring" and "Fat Liquoring pt1" and "Fat Liquoring pt2" ,all published in World Leather. In times past leather was treated with oils and waxes that did not bind to the fibers, would migrate out, and had to be replaced. This was the work of curriers. That business appears to be about gone, since fat liquoring took over.
Conditioning is done to replace any oils (that are lubricating the fibril bundles) that have been lost, (to things like cleaning, stripping, stepping in a puddle, and oxidation, to name a few).
Conditioning is done primarily to adjust the moisture content of the leather. In studies of leather properties, the samples are "conditioned" at standardized relative humidity to adjust the water content. Adding oil to replace lost oil may be necessary if the piece has been treated with something that can remove the fat (like the VOC's discussed above). But if you do not do this, then modern leather will lose little of its fat in normal use.
In a related discussion on AAAC, the member calfnkip, who is in the tannery business, had the following comments
...when the leather arrives at the shoe factory, it is fully fatliquored / conditioned and ready to be made into shoes that are meant to give years if not decades of service.
Under normal use, small amounts of these fatliquors may leach out of the shoe’s leather due to the flexing it’s subjected to when you walk. The quantities that migrate out of the leather this way are pretty small and shouldn’t compromise the integrity of the collagen fibers for some time - - often quite a few years if the tanner has done his job properly. And you are correct that it is not really possible to restore all the fatliquors, greases, waxes and other compounds that are applied to footwear leathers during the tanning process.
He does not elaborate on why is it not possible to restore the fat liquoring, but the problems are: the fat liquoring is performed with the leather in a drum, heated, with a series of chemicals that are not available to the consumer, under pH and ionic strength conditions that are adjusted for the particular liquor and leather. All sides of the leather are exposed. At the end of this process, some of these conditions are carefully altered to complete the binding, extraction of emulsifiers, or in other ways. These cause permanent changes in the leather, which may not permit more fat liquor to be added.
In response to a question on this topic, Steve Gilbert of the American Leather Chemists Association posted this comment
...under normal conditions there is not need or in reality no real possibility to re fatliquor a finished leather article. It is part of a chemical process during tannage.
If you search Science Citation Index, you will find papers describing the uses of humectants in maintaining the water content of finished leather. PEG, sorbitol, and glyercol seem to be the most common.