Nope. Disagree. Look at claim construction in a patent "a fixing means", for example, isn't an implementation it's an element of an idea. A patent application has to include a concrete implementation but the claims - which define the patent legally - are always broader than the specific implementation and will cover multiple implementations that use the inventive concept.
Thus, a new product that's never been made before can infringe an existing patent. The implementation is new but the _idea_ is not.
Proving that a patent's claims cover disparate implementations is how you successfully defend yourself against patent lawsuits. If a patent's claims are ambiguous enough to cover multiple, novel implementations it is by definition "overly broad" and will be ruled invalid.
Claim drafting is a specific broadening process - overly broad claims (I'm coming primarily from a UK perspective [ex-professional]; I can't cite chapter and verse of EU/US but consider myself a well informed layman in those areas). Yes claims must be supported by the description (UKPA S.14, EPC Art.84, no idea for USC) and not cover a plurality of inventions but multiple independent claims specifically cover a multitude of implementations of the same invention.
The claims shouldn't cover multiple inventive concepts (called "plurality" in UK terms), as you intimate, but covering multiple _implementations_ of a single inventive concept is kinda the whole point. An example being drug patents [not my former area] where the functional chemical groups will be claimed when paired with many other standard chemical forms. Another example would be for an allowed compression algorithm that could be implemented in silicon as part of a co-processor, or which could be implemented purely in software [to gain a real technical contribution in the inventive part of course].
FWIW your cited case (discussion here is useful https://www.law.cornell.edu/supct/cert/13-298; I only get an abstract at your link; cf. https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_Intern...) concerns a different issue entirely, that of claims being made to a financial concept rather than an invention per se, basically the contention upheld is that the claims were to a financial fact that falls within excluded subject matter. It's nothing to do with breadth or multiplicity of implementation.
Thus, a new product that's never been made before can infringe an existing patent. The implementation is new but the _idea_ is not.