The first exoplanet detection was in 1992; in my lifetime, "there are no planets outside our solar system" was roughly as supportable as "there is no life outside our solar system" is today.
You seem to be talking past everyone else in this thread because nobody has disputed a single thing you've said however you're ignoring (perhaps unintentionally) the basic statistical reality that if we focus on potentially water- and carbon-rich environments we are as a matter of course more likely to find life sooner.
But the "basic statistical reality" is also "there are a lot more known/accessible planets outside of the zone in which liquid water exists naturally on the surface", which leads to a quantity vs quality consideration for which we don't have enough information to decide right now.
Yes but "we don't have enough to decide" means you have to lean on the single data point you have, not completely ignore it and just try to look everywhere all at once. You have to focus your finite resources and "just pick something" isn't a reasonable path when there's more things to investigate than we could do in 10 lifetimes.
> Or maybe we start with what we know (carbon-based)
But we know more than one thing. One of those things is the Fermi paradox - that the universe should statistically be full of evidence of life, and yet we struggle to find it. That may be evidence we're making the wrong assumptions.
> keep our minds open to other possibilities...
Yes, and I'd argue that means including scenarios like Jupiter's moons in our search. (As a bonus, Jupiter-style planets, being larger and far from the star, are substantially easier to find.)
Like you said, the first exoplanet was detected in your lifetime.
We haven't even had the chance to fail yet, the Fermi paradox is not yet in play when we're considering essentially our first move. To extend an analogy from further up thread, it'd be like looking in the Mariana Trench for un-contacted human tribes after taking a quick glance around the neighborhood and deciding there's nothing else to be found anywhere else.
Here on Earth, we can barely decide if viruses are life or not, and discover new things within our own bodies pretty regularly, despite... a lot of direct access to them. (Example: https://www.science.org/content/article/it-s-insane-new-viru...)
We should be casting a pretty wide net.