Take, for example, the "Chain of Reasoning" section of the Wikipedia page page about the "paradox", which ends with following two steps:
> Since many of the stars similar to the Sun are billions of years older, Earth should have already been visited by extraterrestrial civilizations, or at least their probes.
> However, there is no convincing evidence that this has happened.
The "should" in the first doesn't follow from what goes before at all, and the second is one of the most basic logical fallacies: absence of evidence is not evidence of absence.
And take your own point about "K3 civilisations". Let's lay it out:
1. A "K3 civilisation" is one that controls the energy output of a galaxy.
2. Therefore it would be detectable with our instruments.
3. Therefore the fact that we haven't detected one means there isn't one.
This is just bad reasoning. 2 doesn't follow from 1 and 3 doesn't follow from 2.
The "therefore" in 2 ignores the word "control" in "control of the energy output of a galaxy". It makes an implicit assumption that any civilisation in control of such resources would necessarily do something with those resources that would result in an amount of radiation detectable to our instruments being emitted in our particular direction, whether that's some focused signal directly targeted at us or some massive omnidirectional blast. Maybe they would choose to randomly set off supernova-sized blasts for shits and giggles, but maybe, you know, they wouldn't. For 2 to follow from 1 you need to know that such a civilisation would necessarily produce detectable signals and you don't.
Then, for 3 to follow from 2 you have to assume that every signal reaching our planet that is capable of being detected by our instruments is in fact detected. That is hilariously far from being true. Yes, we have some amazing instruments, including ones that can capture enough light from a nearby planet to do spectroscopy on its atmosphere. But those instruments are not simultaneously pointed in every direction all the time. The exact number isn't knowable but certainly 99 and several 9s percent of the signals reaching the Earth at any one time that we could detect and analyse we are in fact not. You talk of surveys but the idea of "surveying" our galaxy (let alone the universe) sufficiently thoroughly to rule out the presence even of the sort of advanced civilisation that produces vast uncontrolled blasts of undirected energy (and of course there's no reason to think an advanced civilisation necessarily would) with current technologies and funding is laughable.
You can't bootstrap knowledge from nothing. The universe is staggeringly vast and we've barely started to look at it. The knowledge we have at this stage places essentially no limits on the sorts of alien life that could exist or on how widespread it is. If you want to speculate about what's out there, please do. I love science fiction! Just don't pretend it's science and please don't claim certainty when your arguments achieve nothing of the sort.
