Generally, that's a generalization.
Round here it's not uncommon to carry a stage bottle for a shallower portion of a multilevel wreck dive in order to extend the dive by switching to a richer mix when coming shallower. Often this offers the opportunity to significantly extend bottom time while avoiding/limiting deco obligation as well:
Here's a dive on the Stolt or Algol here off NJ with EANx 28 back gas...
Dec to 130ft (2) Nitrox 28 50ft/min descent.
Level 130ft 17:24 (20) Nitrox 28 1.35 ppO2, 115ft ead
Asc to 80ft (21) Nitrox 28 -30ft/min ascent.
Level 80ft 30:00 (51) Nitrox 28 0.94 ppO2, 70ft ead
Asc to 20ft (53) Nitrox 28 -30ft/min ascent.
Stop at 20ft 21:20 (75) Nitrox 28 0.45 ppO2, 15ft ead
Surface (75) Nitrox 28 -30ft/min ascent.
Here's the same dive with a staged bottle of EANx 40...
Dec to 130ft (2) Nitrox 28 50ft/min descent.
Level 130ft 17:24 (20) Nitrox 28 1.35 ppO2, 115ft ead
Asc to 80ft (21) Nitrox 28 -30ft/min ascent.
Level 80ft 30:00 (51) Nitrox 40 1.34 ppO2, 53ft ead
Asc to 20ft (53) Nitrox 40 -30ft/min ascent.
Stop at 20ft 3:20 (57) Nitrox 40 0.64 ppO2, 7ft ead
Surface (57) Nitrox 40 -30ft/min ascent.
Certainly worth staging a tank of 40% in order to shave 18min of deco off your hang, especially if the water is cold and/or choppy - which it usually is here.
In fact, staging and switching to 40% at 80ft lets you out of the water faster than if you carried 02 for deco...
Dec to 130ft (2) Nitrox 28 50ft/min descent.
Level 130ft 17:24 (20) Nitrox 28 1.35 ppO2, 115ft ead
Asc to 80ft (21) Nitrox 28 -30ft/min ascent.
Level 80ft 30:00 (51) Nitrox 28 0.94 ppO2, 70ft ead
Asc to 20ft (53) Nitrox 28 -30ft/min ascent.
Stop at 20ft 7:20 (61) Oxygen 1.59 ppO2, 0ft ead
Surface (61) Oxygen -30ft/min ascent.