I always thought LFU is stated by the SM , but I recently read that it was just assumed because measurements suggested this universality. If thats true, proving LFU violation would not automatically be a hint for new physics.
So does LFU arise from the SM or was it just assumed due to (no exact enough) measurements?
Given the talk link clarifying your real hidden question...
Bonafide LFU means all leptons couple to gauge bosons identically, up to PMNS mixing; of course, they couple differently to the Higgs doublet, given their different masses. In this respect, they are not conceptually different than the quarks.
So, again, LFU violation ("new physics") refers to couplings and effects not attributable to mass and mixing differences which are part of the SM, so, in effect, background. LFU does not refer to a putative mystical property of the SM which would make flavors indistinguishable.
The conceptually muddled talk you refer to strangely stretches LFU to include such mass difference and flavor mixing effects, although wisely caveating minuscule SM loop effects such as 𝜇 → 𝑒𝛾 as non-genuine LFU background. Such distracting backgrounds rely on the smallness of neutrino masses, and are broadly analogous to loop-induced FCNC in the quark sector.
The essential similarity of the three generations is a simple assumption of the SM, universality, discerned early on as a general feature of data, and adopted into the SM, a model of data stressfully evolved into a theory, for simplicity; so far, it appears to hold, unless "new physics" is concerned. Any departure from it would be a violation/modification of the SM, which appears quite unforgiving to this sort of thing.
