Split leather is a great surface to dance on -- so much so, that before dance boots with split-leather soles were available, country/western dance competitors used to glue split leather onto the outsoles of their boots for ease of motion combined with improved control. This ease of motion enables you to get better results dancing with less strain on feet, legs, and joints.
Dance shoes have the added advantage of being lighter in weight than most conventional shoes (so that you work less while dancing) and more flexible (so that they form around your feet with less pressure than conventional footwear). They are also designed with more padding in the insole than many conventional shoes, so that your feet are comfortable dancing for longer. Finally, they are generally designed with more toe room so that your feet can move comfortably without pressure.
No product has yet been designed or manufactured which will do everything without any disadvantage; and dance shoes are no exception. They weigh less than conventional shoes because they are made of lighter-weight leather. The split-leather sole performs better because of its napped ("fuzzy") surface. The "trade-off" for these advantages is that dance shoes are not constructed of heavy-weight leather intended to stand up to repeated hard, punishing wear (rough pavement; exposure to the elements, especially moisture; exposure to grit which can clog the nap of the sole).
Leather and water are natural enemies, and no manufacturer of quality leather footwear would ever be enthusiastic about your wearing unprotected leather out into wet weather. Nor do we recommend wearing any footwear through wet weather to a dance, then wearing the same shoes on a wooden floor to dance in. It isn't good for the footwear, it isn't good for the floor, and it's not helpful to the other dancers as the wood absorbs the moisture and becomes slow and difficult for all to dance on.
We believe the advantages for the dancer in weight and flexibility are well worth the use and care of dance shoes as dance shoes. We also hasten to point out that split leather is a reasonably sturdy material and that the shoes don't instantly "self-destruct" if you step out the door. We have numerous customers who "retire" old dance shoes or boots to casual streetwear. Please understand, however, that the shoes don't perform the same as dance shoes which are kept for dancing, and that they should not necessarily be expected to wear the way a conventional-weight shoe would for streetwear.
If you must wear your shoes for streetwear, they will then work best for dancing if you brush them periodically with a steel brush reserved for this purpose. Try brushing with the nap at first, but if this doesn't restore the "fuzzy" surface, brush against the nap. You can even try a circular motion, if necessary applying moderate pressure to raise the nap.