Taken literally (which is more or less the EASA line) this is the same as saying that an A&P or an IA is dumb, cannot read, has no idea how a plane works, and has no authority to sign off any mod other than a Type Certificated add-on accompanied by full drawings for that specific serial number range airframe.
I have never thought of the people of the maintenance world "mechanics" to generalize (though I know there are many types) in this context. Many of the modifications I am asked to approve originate with "mechanics", and are excellently thought out, and very workable. I nearly always approve them with little change.
That said, every type certificate contains a section called "certification basis". This defines what is the minimum design standard applicable to that type, and that becomes the minimum standard to which any mod must also qualify, and demonstrate compliance. Though I agree that "mechanics" are very skilled, it is possible that they are not a conversant with the design standards, and how they are to be interpreted, and applied. That's where the FAA "DER" or TC "DAR" (very similar roles) come in.
Added to this, you will see a statement at the bottom of STC's requiring the installer to assure that the installation of that mod, does not create an unsafe condition in the context of the other mods which may already be installed on the aircraft. This is because the original type design showed compliance, and the first STC did also, but it is very possible that the second STC was not assessed for design compliance in the context of the aircraft with the first STC installed, the permutations would be very numerous!
An example of this would be; could you install a Horton STOL kit on a Cessna 185, which already has a Robertson STOL kit installed? Surprisingly, in some cases, yes! In an other case, I specifically approved such an installation.
Another much less comfortable example is the installation of an STC apporved TCM 550 engine to on a Cessna 180, in place of the O-470. The 550 has a much greater fuel flow, but the 180 airframe has demonstrated that it can provide that fuel, so compliance with the fuel flow requirement was found. However, the "least favourable attitude for fuel flow" used was probably not the higher pitch attitude attainable with a STOL kit, or VG kit. Yet there are many examples of aircraft with combined mods. I can tell you from personal experience, that in at least two Cessna 180's so modded, it is possible to fly the aircraft at full power at a pitch attitude so high (and much higher that the original) that fuel flow for the larger engine cannon be maintained, and it quits. 'Been there, done it! This is exactly the situation which could exist with a pilot straining the plane over the trees on takeoff - and then it quits!
The installer of the second STC, had not considered the iner-relationship of the second STC, with the first, and an unsafe, and non compliant aircraft was the result.
I realize that this is a far extreme situation from that presented in the original poster, but it is important to conssider that a DER/DAR is the person who's job it is to establish that ALL applicable design requirements for a mod have been considered, and met. "Mechanics" perhaps
can do this, DER/DAR must!