I'm a bit late to this party, but I voted for a run button, but for reasons I haven't seen discussed here:
Movement in fighting games is one of the basic fundamentals. You need to be able to move efficiently to dodge, defend, play footsies, and attack, so movement should always be the most efficient input possible. Any beginner should be able to do all of the movements the game allows quickly and easily. That's why all of the movements are the same for every character, and are one button press (except for dash/backdash, but I'll get to that in a minute). Duck is down, jump is up, up/forward, or up/back, step backward is back, and step forward is forward. At this point, we run out of directional inputs and have to use other things, so block (which is could be argued is a movement, but it's definitely a fundamental) becomes a dedicated button. Dashing either way is a simple double tap, which is something pretty much any child could do. When you make run F,F, BL, you're essentially turning it into a special move, which has a slightly higher barrier to entry. Yes, it's a rather easy input, but it still required execution some people won't have. In fact, B, B and F, F inputs are the number one reason I play with a pad, because I can't seem to get left, left to come out reliably on a stick. Yes, I could put in the time in practice mode, but I can do it easily on a pad and I'd rather spend the little time I have available on learning to counter and/or punish specific things from other characters than trying to learn a basic movement on a new controller.
With regular special moves, there are ways around them. If a beginner has a stick and finds it especially difficult to do the motion for Scorpion's spear from one side or the other, yes, the correct option is to practice until it works, but not everyone has enough time to devote to that, so they also have the choice to play a character whose specials don't have the input. If they can't run, though, they don't have that option, which means they have to either ignore the run mechanic altogether or spend a bunch of time grinding it out in practice mode before they can really start learning any of the basic principles of the game (and have any fun fighting). That makes us less likely to attract new players and keeps our community smaller.
In addition, it really goes against the basic principles of fighting games - movement should be easy and efficient, and maximizing damage should require execution and skill. The better you get, the more reliably you can damage your opponent. You shouldn't have to practice and level up to incorporate a basic movement mechanic.
