Taking a cue from my uncle, a craftsman, I have many wooden mallets. I made many of them of different species. I use a softer wood mallet to tap the harder project wood, so as not to damage the project wood. When a head becomes too damaged (seldom), I replace it. Some heads are not perpendicular to the handle, about 8 to 10 degrees off, to accommodate a slightly different drive when needed. I have a wide variety of sizes and some have a wedge shape on one face. A few I've added cow hide straps simply for decor, like a tomahawk. On the brighter side, those of 4" or larger heads are attitude adjusters, not mallets, and more for display than use. Many I have are tree limb heads on tree limb handles, no two alike, and I've learned to distinguish them for particular uses. Besides, why waste a good tree limb by trashing it? Make a mallet.... or an attitude adjuster.
I also do upholstery work. Leather or rawhide mallets are used to drive tack strips into place and to attach front arm panels, and the like, onto the furniture. The tack strips and panel structures are under the fabric, so the leather mallet, though hard, does not damage the fabric when driving these tack/nail applications. I also have a series of short wooden plugs (3" long dowels of different diameters), wrapped in scrap fabric, that I sometimes use as buffers between mallet and fabric-structure application. As with anything, you can go over-board and tap too hard and damage anything, so some care is required when tacking/nailing through fabric, this way. Vinyl hammer heads (tack hammers) are used for decorative tacks, so as not to damage the decorative tacks. I suppose small wood mallets may have been used before vinyl came along.
Sonny