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.