Yep as others have said , sport handling mode is especially great for the following:
a. allows slip of the wheels to allow the car to power slide for a few seconds. it is very gradual in allowing your car to slip out of it's natural cornering axis and then brings it back in line gradually. almost makes you look like a pro driver ! remember with all power slides though to counter steer into the slide and control it with throttle input and dont hit the brakes for a good quality slide
note also that sport handling may affect your steering weight, engine throttle response and holding revs higher so your car turbos are spooled and ready ! (it does on my c63s , cant remember on the gla 45)
b. on the newer 45 models from 2017 at least (the one I used to own) , no need to turn sport handling mode for launch control but if you want a more interesting launch (and faster launch) then press this button ! btw all you needed for launch control was the car to be in sport mode
c. as mentioned , for driving in snow , this does make the drive better as it allows controlled wheel spin , but prevents you spinning your car around.
d. I swapped my gla 45 for a c63s wagon and sport handling mode on that car is a completely different prospect! the 45 I could go around corners and all 4 wheels would spin and it was too easy to do power slides , on the 63 , the rear end slips out a **** of a lot with no effort at all on the gas pedal!