If that's the case your over-reaching or overextending your jab (falling to far onto the front foot/hip), your right foot should be underneath your rear shoulder when your jab lands and if your having to shift it forward, it's your right foot that you are leaving behind when you are stepping into the jab by falling to heavy onto the front foot. Your right cross is a longer reaching punch than is your jab, hence: jab into range, set, then throw your cross. You DONT want to get into the habit of your right foot sliding forward when you throw your cross.
All true and very useful info in your post. The takeaway is, move your right foot forward when you need to and don't when you don't. You may even need to take a half or full step (maybe two) BACK before throwing your right to make it connect with your opponent. It all depends on where he is now AND what he does after (where he moves after your first punch).
You'll still have to take a step forward with your left and right foot before throwing your right sometimes (often). Lots of opponents like to move or shrink backwards or sideways when they see you start any punch (even a jab) or feel it connect. If the jab lands, it can bounce them backwards a tiny bit plus they shrink as a reflex, and you might lose penetration with your right hand (because it can be longer than a jab but not THAT much longer to reach a retreating/pulling-back opponent without any footwork). This happens all the time.
Also the jab can be incredibly long if
you turn almost sideways and use it like you would in swordplay. This jab catches people off guard from long range (because of how incredibly long range it is) and if you hit someone with it, you're not going to be able to get good penetration with your right hand afterwards most times because they're already on the outermost boundary of your general reach (but they didn't realize they were still within hittable range, because a lot of people don't know how to throw their best jab).
But yeah, I get what you're saying about a regular jab within or inside normal distance, there still will OFTEN be proximity to shoot your right after the jab and hit the guy after your jab lands (which is why the 1-2 is likely the most winning-est combo out there). You have to manage the distance depending on the relation of where you are to where he is after you jab- it's not set in stone for every opponent or even for the same opponent every exchange.
If you don't need to step, I agree it's best not to step. The problem here is it is very useful to step with your right (and touch down) before throwing your right hand if you need to, and a lot of people don't know how to or if it's even ok to do in boxing. Yes it's ok, it's a very useful technical detail taught in boxing gyms, (one that most people would/do not figure out on their own) but like anything, you don't do it ALL the time, just when its beneficial to.