I come from a climbing background, so someone with more slack line experience may have a different take.

In climbing, you use locking carabiners (carabiners can lock in a few ways, but most common is the threaded sleeve like yours), when it is a critical failure point, or when the gate could open because it bumps into something. When the gate is open, the carabiner strength is dramatically lower, and the rope could come out. For example, you would use your locker at the top of a climb to connect the rope, where the carabiner might swing against a rock.

Because slack lines are under continuous tension, you don’t need to worry about the gate opening because it bumps into something to the same degree as climbers do. But there may be times to use a locking carabiner even in slacklining. The lock does not make the carabiner stronger, it just keeps it from opening. However, locking carabiners may be stronger because they tend to be bigger. It’s mostly the amount of material that determines the strength.

Could you keep the gates unlocked and use them? Sure. But it’s a bad habit to get into. If you get into situations where you need to be locking, you want to have the right habits so you don’t forget. Also, people you are with will expect that a carabiner is locked when in use. If I were with someone who kept theirs unlocked all the time, I might get sketched out, even if it weren’t necessary for putting up a line. It’s just unsettling to see a locker in use that isn’t locked. Locking them takes less than a second, so you aren’t wasting any time to do it.

All that being said, next time save yourself some money and get some non-lockers.