I think that view is a little too simplistic. There are some powers you probably just shouldn't give to governments, ever. There are some powers that are fine to give to governments, because they're unlikely to be abused, because abusing them confers little benefit to the abuser.
Then there is a third class of power, where it's useful for the government to have it, but abuse of it can be really bad. So you need to make it really hard to abuse that power. Maybe using the power requires a lot of people to agree. Maybe a list of difficult-to-forge and difficult-to-abuse conditions need to be met before that power can be used. Maybe the power is designed so a lot about how it is used ends up being public, so people can audit its use. And so on.
But I think if there's a power that is likely to be abused by government, and really hard to put checks on that (ab)use, then the government just should not have that power, no matter how useful that power might be.
The problem with assuming that last bit isn't a big deal because they're the "good guys" is that even if they genuinely are the good guys, you never know who is going to get elected during the next cycle (or the next-next, or the next-next-next, or...). They might not be the good guys, but they still get to use that power, and certainly won't pass laws to take that power away.
Often the alternative to giving a democratic government power really is for nobody to have that power, and in many other cases the alternative is for the power to be decentralized, so that many people have some of it.
For example, we might give a democratic government the power to tap everybody's phone calls at once, but if we don't, that doesn't necessarily imply that undemocratic, unelected oligarchs, or anyone else, is tapping everybody's phone calls at once. There might just be nobody who has the power to tap phone calls, as is the case with secure free software running on trustworthy hardware, or there might be many people who have the power to tap only a few phone calls.
And we might give a democratic government the power to assign workers to jobs, for example, as the Soviets did. Alternatively, undemocratic, unelected oligarchs could assign workers to jobs, as in a coal-mining company town; but an additional possibility is that workers and employers, or unions and employers, negotiate with one another, each limiting the power of the other.
We might give a democratic government the power to decide what's for dinner each day, which sounds ridiculous but is exactly the standard practice in kibbutzim and in school lunch programs in democracies. Conceivably, undemocratic, unelected oligarchs could decide what's for dinner each day, though I don't know of any examples; the usual alternative is for each family to decide what's for dinner each day independently, though in many cases this degenerates to an undemocratic, unelected head of household deciding. Often enough, some household members prefer school cafeteria foodoid products to the results, despite having no say in that decision-making process either.
The alternative to giving a democratic government power isn't 'nobody has power'.
The alternative to giving a democratic government power is ceding it to undemocratic, unelected oligarchs.
When a democratic government has it, you get some say in how it is used.