I'm pretty sure they are paying their taxes. To pay the minimum allowed by law is their fiduciary duty.
Assuming you're from the US, every year you have the choice to take the standard deduction or itemize. Do you ever feel guilty for choosing the option that lessens your tax burden? Why would you hold a company to a higher standard?
If you think that companies should pay more taxes, then push your government to close the loopholes they're using and/or raise taxes. If you're counting on people to 'do the right thing' when they're directly incentivized not to you're going get nothing but disappointment.
You're talking about incentives which is a different discussion. There are incentives that go the other way too: evading taxes looks bad, it's bad for business if society crumbles for lack of revenue, morally it's wrong to benefit from infrastructure, education, etc and not contribute back. But that's not the point I was addressing.
If I owned a company overpaying taxes I'd seek to have them acquired (priced using a tax-efficient income assumption) or management replaced. Suing would be unlikely.
That said, I agree with your general point that no fiduciary obligation is likely violated. It's just bad business.
What you're proposing is referred to as 'Social Darwinism'. In this application it is used in a pseudo-logical fashion to beg the question entirely and falsely imply the justification of a lemma.
Your argument is as follows. "If you believe in (1) [natural selection applied to companies], then (2) [causal hypothesis: '1' leads to 'type'], meaning that (3) the [companies of type] we see now are the result of [natural selection applied to companies]."
I hope it is apparent when you look carefully that the 'companies of type' we are seeing now would be simply the result of natural selection in any case, that there is no support for the causal hypothesis presented, and that the causal hypothesis is not in fact a logically necessary implication of the original lemma.
The reason that this might feel meaningful, rather than be at first glance a tangle of errors, is that it involves the juncture between a hypothesis for which you feel you have evidence (and do!) with a core belief. Your hypothesis: "companies that do better at minimizing taxes are more likely to survive than those that don't." Your belief: "markets are efficient and the best economy arises when companies are allowed to compete without interference."
The difficulty here is in the confusion of the two intellectual contexts. Natural selection is a descriptive theory about how what is came to be. Market libertarianism is a prescriptive theory about how what should be can come to be. They are not interrelated. Under condition of Soviet Market, natural selection will still exist. Even if regulatory capture helps a company survive instead of perish, libertarian theory still advocates against it.
If you believe in natural selection applied to companies, then what we have here is the natural and almost predictable extinction event of those companies that over-optimized on minimizing taxes.
However, the belief in "natural selection applied to companies" is essentially meaningless once you decouple it from action or advocacy; coupled to advocacy, it is incoherent. It inherits absolutely no scientific justification or intellectual rigour from biology.
Minimizing taxes as a financial optimization strategy have everything to do with competitive advantage. If we were genuinely looking to take lessons from biological history, it would teach us that subsequently perishing as a consequence of that adaptation is entirely natural and normal. 'Natural selection' is whatever happens. It is often conflated with various notions of progress, merit, laissez-faire, et cetera, but seldom honestly.
Selection bias is a real thing, however. For example, "All politicians are corrupt" doesn't mean they all are, but given corrupt as a competitive advantage, the ones that weren't corrupt are not successful enough to be known. You don't have to be corrupt to be a politician, but you might have to to be a successful one. Businesses are much more like that given hyper competitive environments.