And you are absolutely right about the "who cares" stance. If our estimates of DM and dark energy are right, only 5% or so of total energy in the universe is in SM physics (visible matter). How can we be satisfied with that?
Hossenfelder is pretty clear that internal inconsistencies are real problems. The problems she dismisses as pseudo-problems are attempts to explain the values of free parameters or otherwise try to explain the "origin" of the laws of physics. This doesn't fall under that.
This is begging the question. Of course explaining the values of free parameters is a hopeless endeavor (it's in the name), but we don't actually know which parameters are free. We know which parameters are free in the standard model - but the standard model is just an effective theory. Radical instrumentalists like Hossenfelder might be satisfied with that, but a scientific realist shouldn't be.
But, I'm not sure this really addresses the point? Like, as I see it, the basic question here is, which problems sufficiently require resolution that looking for that resolution is likely to bear fruit? And it's hard to see how "certain particle masses (or other seemingly-free parameters) seem small/large" qualifies. Small or large by what standard? It's a lot smaller/larger than 1? OK, but what's "a lot"? Who's setting the scale here? Ultimately the universe's scale is the only one that matters here, and if we find its numbers unusually "small" or "large" that's just a matter of incorrect expectations on our part!
Like, if you want to say we should be looking for axions or magnetic monopoles on the grounds that a literal zero is suspicious, then, sure, I guess zero is fairly special and suggestive. But I don't see that there's any sense in trying to find explanations for numbers being "unusually small" or "unusually large" when there's nothing but our own expectations to mark these magnitudes as "unusual".
I see what you mean and agree that talking about "small" or "large" fundamental constants doesn't make a whole lot of sense - but that's not what's going on with particle masses or other hierarchy problems.
The effective masses we actually measure are not the (presumably fundamental) bare masses we would measure at infinitely high energies. They're adjusted by, in a very rough sense, the energy content of a particle's interactions with surrounding fields - an electron's effective mass is its bare mass, plus the contribution of its one-loop self-interactions, plus the contribution of its two loop self-interactions, and so on. Naively we would expect those contributions to be mostly uncorrelated, and the effective mass to be of roughly the same order as the highest-weight terms in the perturbation series.
When physicists say that a mass or coupling constant is too small, they mean that it's small compared to the terms in its perturbation series, which means that something is causing them to very nearly cancel out. It's as if we had what we thought was an ordinary random walk (which we would expect to have a magnitude scaling as sqrt(N) after N steps)... that reliably hovered around 3.
Still, clearly the Sterile Neutrino hypothesis was worthy of investigation based on her own reasoning and previous statements.
Scientific community. Via a process of peer-reviewed publications. Not via blog posts and Youtube videos.