Well, let's think about what cancelling tricks do, before we come to a conclusion of how important it'll be for your build. What happens is that game prevents you making an animation from 180 degree turn. It's a short turn, and it takes very little commitment. The running pivot-cancel takes a higher commitment, but it's much easier to pull off, and provides a much bigger window to cancel. If you are doing any kind of pivot-cancel, you are, at the most basic level, switching one commitment for an ideally smaller one. At a secondary level, it also switches the location of your back quite rapidly; it invalidates most punish attempts if done correctly. Finally, at a tertiary level, it saves a casting of a spell, but keeps some of the threat. We can say that when you are doing a pivot-cancel, you are doing these three things.
How useful are doing these three things? Obviously, it depends on what sort of spells you are casting; since you are asking about Pyromancies, let's examine some pyros. Pivot-cancelling Fire Surge is impossibly normally, and can only be done with a running pivot-cancel. However, the commitment is so low, the threat so minute, and the value of saving a single casting so negligible, pivot-cancelling it is worthless. Similarly, when we think of Great Combustion, it has similar properties, and similarly worthless to pivot-cancel. When we get to the larger spells, we can say there is some worth to pivot-cancelling; the Fireballs, while not strictly necessary to pivot-cancel, can have some usage can help avoid a backstab when you try to land a straight downward fireball. If you want to become better at being a Pyro, it's well worth learning every trick to get the most out of your Fireballs, so while you won't need to, it's good be able to pivot-cancel these consistently. Being able to pivot-cancel anything with a larger commitment is almost a necessity. If you try to cast Fire Tempest, it leaves your back very open, but the pivot-cancels make harder to tell when your back is in fact ready to be stabbed. It can really make all the difference with the larger spells, but it's quite possible to have a solid, vanilla Pyromancer that uses only Great Combustion, and Great Fireball, but making the jump from good to great takes those other spells.
A rule of thumb is that anything that has large commitment, you must be able pivot-cancel it if you want to use it. A few exceptions exist, for example the various, but generally useless, Fog spells don't need to be cancelled. Nor does White Dragon Breath, or Chameleon. In fact, Sorceries are essentially free of the need to pivot-cast, but they tend to be pretty stat intensive. The Dark Sorceries effectively fill a niche that Sorceries didn't have before: it gives something for the 30s, and might really help make casters more viable at SL100. The Soul Spears, and the very good capstone White Dragon Breath are hard to squeeze in for the arena, but I'll try to see if I can make anything happen them work for me.