As noted previously, they tend to pick up dust and the two-piece construction (vamp and quarter) leaves side openings that let sand in the sides (not present on Medo-Persian shoes, which were probably like Plains moccasins in construction, i.e. one-piece uppers). Since I'm now aware that period leather likely had a rough finish more often than not, the dust is not an issue. The side openings are but I'm looking into stitching them up or perhaps adding fabric panels.
In the meantime, another quick way of improving the boots' appearance, after you've cut the fringe off, is to replace the laces with flat suede thongs. Art stores such as Michael's (in the U.S. and Canada) sell strips of 1/2 by 36 inches, which is just about right for our use.
Undo the laces and pull them out. With a seam ripper or a craft knife with an angled blade, cut the stitches holding on the upper strip of leather forming the "tunnel" through which the lace was inserted. There are two seams, one inside and one outside of the shoe.
To the now-exposed upper part of the quarter, add vertical slits through which you can insert the thong - not, of course, too close to the upper edge; about a third of an inch away should be safe. I find a double slit at the back of the quarter and a single slit on each side of the front to be sufficient to hold the thong in place while leaving most of it exposed (as was the case with the thongs on Achaemenid shoes). Tie the thongs in square knots rather than bows, and trim them as you see fit.