The problem there is that if you wait for the right technology to appear, it may never happen, because all of the effort and resources that would’ve been put in

The problem there is that if you wait for the right technology to appear, it may never happen, because all of the effort and resources that would’ve been put into researching and manufacturing engines for interstellar ships would’ve instead been put into something else. There’s still a chance that we stumble upon the right tech anyway, but the chances are greatly reduced and even if we do, it’ll likely be far later (centuries even) than it would’ve been had we been had we actively been developing said technology. From my perspective, it makes more sense to risk obsoleting previous missions and send ships as soon as it’s possible to do so because it’s a far better outcome than waiting for tech that never came and never sending a mission at all.