I'll answer your "hows": with higher iso's, fast glass, and in camera settings.
Not to be difficult, but how does this resolve the lights color cycling, white balance, and achieving effective shutter speeds up to the duration of the flash (often 1/1000s or much faster)?
For example, your first shot shows:
Lens (mm): 35
ISO: 1600
Aperture: 2.5
Shutter: 1/200
and you second image is at:
Lens (mm): 35
ISO: 1600
Aperture: 2.5
Shutter: 1/250
A shutter speed of 1/200s or even 1/250s will not cut it for even the relatively slow High School action sports. Maybe I could boost my ISO to 3200 or higher to double my shutter speeds (OK, to half them, actually), but my customers would balk at the noise (even with a D3 or 1D MkIII).
Shooting with strobes, my effective shutter speed is at its slowest 1/1100s (but it can be much faster with the right strobes or flashes) which even then is only marginally acceptable for some sports.
I'm not diminishing your accomplishments or abilities - only trying to make the point that even WITH higher ISO's, faster glass and camera settings (the standard ways to deal with any photographic issue), you will not overcome the issues inherent in shooting ambient that will be very effectively dealt with by adding artificial light. You will still have light color cycling; you will still have shadows and tough WB issues; your colors will still appear relatively dull and flat - all at least compared to what is achieved by having artificial light at least 3 stops over ambient.
Maybe you're comfortable with this, and that's OK. Many of the groups for whom I shoot are not and as a result, it's my job to figure out a way to eliminate these issues. This is my definition of a "competent" photographer - one who delivers the goods to his customer's specs the first time and every time he/she is asked to do so, regardless of the quality, color and amount of light available at the event.
To make the outrageous statement that "A competent photographer should know how to improvise with the available light given." when you don't cover sports where the action is a lot faster than MMA is a bit narrow-minded and inflammatory, at least IMO.
Peace out,
Dennis