It has been shown that they can implying their own energy to their bodies, this is why you have them raise their battle power or going at full power. The best example is goku has a kid controlling the flow of his to ki to the maximum to pierce threw king piccolo and kill him. The so called contradiction you have stated is not, its simply misunderstanding.
"where characters have shown visibly more power with their Kamehameha than they're capable of physically. Such as Goku failing to damage a wall with his kicks and punches, but could blast a hole though it with his Kamehameha."
You fail to realize, that the Kamehameha for example, expels more of the users internal power and throw's it at their opponents. Of course their regular kicks or punches would be weaker in comparison to their non-powered up state since they are expelling this ki as a projectile attack rather than using it to amp their bodies.
They can channel their own ki that is already in their bodies to enhances their physical stats. The higher the ki, the higher the physical stats of the user. Without ki, their natural bodies durability is low and losing "ki" greatly weakens their overall physical stats.
According to the UES page, if they do a feat that is with ki or with physical stats, it is assumed that they have at least that level of physical stats that the feat has demonstrated.
If there is a disagree option put me on that, if not the second best would be neutral.