Tossing around rod tapers to define the performance of a rod is misleading. Unfortunately it's not the fly fishermen who created this problem but the rod mfgs.
Rod taper defines the flex profile - not stiffness - so a fast action taper does not necessarily mean the rod is stiff just as a slow action taper does not mean the rod is soft. Recovery rate and power define the stiffness or softness of the rod. Action simply defines the bend profile.
The problem stems from the fact that in today's terminology, action is used to describe the overall performance of the rod, lumping flex profile, recovery and stiffness/softness all into one generic term - fast, medium or slow - based on a specific line rating.
Example, in today's terms you can have two "fast action" 4wt rods. Rod #1 has a soft, flexible tip, followed by a medium stiff mid section followed by a stiff butt section (a traditional fast action design) and rod #2 has a medium stiff tip followed by a stiff mid section followed by a super stiff butt section (modern fast action design). Both rods have the same flex profile (fast action) but rod #1 will feel softer than rod #2. Irrespective of line, rod #1 provides an advantage fishing in close because it has more tip flex. A specific example would be comparing the 8.5 foot 4wt Winston BiiiX and Sage ONE rods. Both are fast action but both are distinctly different rods.
Before the introduction of super stiff graphite rods designed for high line speeds and shooting the entire fly line, slow action rods were the rod of choice for casting longer distances (50-70 feet) and slow action rods were generally heavier line sizes. Tips and mid sections were somewhat stiff and the flex was predominately in the butt section so the overall design provided the power and backbone to carry the heavier line and get the distance. The stiffer tip and mid sections kept the rod from excessive deflection during the cast, which helped maintain accuracy and power. Because the rod flexed in the butt section, the rod was "slower" to respond so the casting stroke needed to be smoother and slower but this did not mean the rod was soft.
Fishability is the key characteristic completely overlooked by everyone. By taking rod #2 above and overlining it you can change the casting feel (i.e., flex profile during casting) to the same as rod #1 using a lighter line but it won't change how rod #2 responds to a load (a fish) under fishing conditions.
Softer tips are better suited when fishing in close quarters, as it help protect lighter tippets and also helps prevent the fishermen from ripping the fly out of the trout's mouth if using heavier tippet. Putting it point blank, "slowing" a rod for casting sake by using a heavier line does diddly-squat when fighting a fish. A twelve inch brookie in current applies the same force to a softer fast action 2wt rod with 2wt line as it does to a stiffer fast action 2wt rod overlined with 4wt line to make it easier to cast. In this instance the softer rod is much better suited for fishing especially in close quarters and when buying a rod this is what you should be considering.
The bottom line is there are more rod configurations available today than ever before so there is no need to overline or underline a rod, especially for trout fishing, if you bought the right rod in the first place. If you bought a 3wt rod but need to overline it in order to cast it at short distances or handle larger flies, you bought the wrong rod.