And it's less about abilities during the fight as it is off-stage stuff. Summoning minions to send after the party or teleporting away after a confrontation.
That's not 'off-stage stuff'. That's on stage stuff. The fact you've already got the distinction somewhat confused suggests to me I'm right about the reduced complexity being an adjudication problem that is going to lead to railroady behavior by the DM.
"Off-stage stuff" concerns actions taken by the monster that do not directly affect the PCs and which the PCs could not directly witness and which does not imply necessarily that similar things should happen on stage. The PCs can only learn about off-stage stuff indirectly, by observation, or by having the event related to them by an NPC.
1) The monster summons minions to send after the party - On stage.
2) The monster teleports away after a confrontation. On stage.
vs
1) The PCs enter a room. It happens to have minions in it. - Off stage.
2) The PCs discover that the monster killed a NPC within a locked room. - Off stage.
The big problem with running off stage without reference to the rules is that it leaves the players basically unable to reconstruct what really happened and to draw conclusions from it. How did the monster get into the locked room? Can it teleport? Can it turn ethereal and walk through walls? Did it have a key? Did it trick the occupant into letting it in? Is it still hiding invisibly in the room? When DMs state something happened offstage without mentally referencing the rules, they are depriving the scene of the artifacts of concrete actions. Things just happen because, which is wholly unsatisfying as a player because there is no way you can do anything but just follow the story along.
An example of why this can be jarring is Jack's cut scenes when Shepherd first goes to rescue her in ME2. During these cut scenes she single handedly destroys several powerful robots at the same time. This implies that she would be an extremely powerful crewmate. However, in actual game play, particularly initially, Jack is not nearly so powerful. The cut scene implies abilities for an NPC offstage that onstage that NPC doesn't actually have. That's just bad design IMO.
More relevant to PnP, consider the case of a recent murder mystery episode in my ongoing campaign. The murder was done Agatha Christy style, with the evidence suggesting a series of events that did not actually occur. The false series of events was created using some simple magic tricks available to a low level Wizard. The exact spells cast the murderer where known to me and were within the actual capabilities of a wizard of that level, including duration, number of spells of a given level that were used, and so forth. Each spell use tended to create artifacts in the shared imaginary space that could be discovered. For example, the fact that the body stank could be used to determine that the victim had first been paralyzed by Ghoul's Touch, which proved that the murderer must have been a magic user. Even deeper in to consistency, Ghoul's Touch was employed because I know that the murderous NPC could not have dealt sufficient damage with a dagger to kill the dead NPC with a single blow unless the victim was immobilized. It also had other concrete effects - neutralize poison removed the stench, spells like 'Speak with the Dead' could be adjudicated fairly based on my knowledge of exactly what had happened during the murder, and as it turned out, the fact that an NPC I hadn't considered as a witness could see through illusions was critical to the particular method the players used to solve the crime, and so forth.
A DM that needs something to happen - a murder by an NPC - but which doesn't have a limited set of known tools to accomplish it, is less likely to create a followable series of events. Things happen because 'plot', and instead of thinking all this out ahead, the answer is generally either, "No.", or the "NPC gets away because 'reasons'."
