In descending order of importance, here are reasons why your attire matters:
Range of motion
Uniforms are cut to provide range of motion for the joints. Skinny jeans and Western-style suit jackets restrict your range of motion in ways that loose-fitting or stretchable clothing do not.
The manner in which clothing is worn also matters. If you wear your pants around your knees, don't expect to be able to run or kick well.
Proper body development
Clothing designed to look good can create problems for your body development. For example:
- high-heeled shoes change the forces on muscles, tendons, and ligaments throughout the body.
- corsets restrict breathing
Even if you don't wear these while actively training, their effects still matter.
Clothing as a weapon
You can use either your own clothing or an opponent's clothing against that opponent. For example, you can grab it, you can choke with it, or you can tie up limbs with it.
For grappling-based martial arts, the uniform plays an important role in preventing the transmission of skin infections which can be viral (herpes), fungal (ringworm), or bacterial (staph). Your skin is one barrier to infection, and the uniform is another. Unless you and your training partners are scrupulous about hygiene, this is an important consideration. Training half-naked may provide fewer advantages to your opponent, but it presents more hazards to you as well.
Uniforms should be designed to last. Most normal clothing will rip or tear under stress from many martial arts activities.
Although appearance is not a primary consideration for uniforms, it does affect whether your training partners stick around, which does matter to you.