>The sooner we launch one, the sooner our descendants get to hear back from it.
Not necessarily. Or more precisely by the time they hear back from it the information will likely be completely redundant.
At present all our mature propulsion technology is very much focused on planetary usage. Rocketry is the only one at all suitable to operating in space, and it's *horribly* inefficient in terms of specific impulse, which will be *the* deciding factor for interstellar travel. Ion drives show immense promise, already completely trouncing chemical rocketry in terms of specific impulse, but it's a technology very much in its infancy and the absolute thrust current engines can produce is miniscule, useful for little more than station-keeping and lining up gravitational slingshot maneuvers. If we launched an interstellar probe with today's technology then it's quite likely that a second probe launched 50-100 years from now would be able to make several round trips before today's probe ever got anywhere close to the target. For a mission whose expected payoff is centuries away that sort of thing is well worth considering. Much like Voyager making its pokey way out of the solar system, the value of an interstellar probe built on current-gen technology would be primarily in learning about the beginning of the path, not the destination. And unless there's some completely unexpected navigation hazard in the gulf between stars there's unlikely to be much to learn worth the cost of the probe.
Now what might be an interesting mission with current or near-term technology is a gravitational-lens telescope - rather than sending a probe towards Kepler-186f we send a telescope "eyepiece" in the opposite direction, and when it reaches a distance of only about 700AU (0.011 light years, ~10x Voyager 1's current distance) away from the sun we could start to use the sun's gravitational field as an immense lens in a telescope so powerful we could count the pebbles on 186f's hypothetical beaches. Maybe even individual grains of sand. Not to mention everything else we might see in that general direction. The downside to such a telescope is that it's extremely difficult to substantially change the target. With a telescope 700AU long even a few degrees of change requires moving your eyepiece across a distance rivaling Pluto's orbit. Still, with a clever flight plan we could get immensely detail information about dozens or hundreds of other star systems as our eyepiece slowly swept out a few degrees of motion. The only real question is, is 186f really interesting enough to be the first target? I would imagine looking toward the galactic core would offer far more interesting things to see.