What does "pulling apart" actually look like though physically? At that scale can we just say "you add this much energy to the system and it creates a quark antiquark pair" and leave it at that?
A rubber band that breaks into two different rubber bands is a metaphor. Whatever is really happening at the hypothetical sub-quantum scale that manages these interactions will be much weirder.
One could argue that it isn't, which is why I described the viewpoint as heuristic. It's not intended to be a comprehensive explanation of everything to do with strong interactions. It's just a heuristic way of describing why adding energy to a hadron doesn't help the quarks inside to escape, the way adding energy to an atom can help the electrons inside to escape.
Gluons? Yeah, you may have a point on that one...
I did say the viewpoint was heuristic. It's quite true that it isn't necessary; you can, as you say, just describe what's going on as adding energy until a quark-antiquark pair is created.