The problem is, the government that launches such a probe will almost certainly not be around when it arrives, tens of centuries from now.
There is no known technology that can get a probe to Proxima Centauri (nearest star) in less than 4,300 years (i.e., velocities of >c/1,000). Just doesn't exist; too much mass and energy are required that that amount of delta V.
The fastest spacecraft ever built by man, 'Voyager 1', traveled a mere 15 km/sec (which is c/20,000). If aimed correctly, it would take 'Voyager 1' a mere 8,600 centuries to make the trip.
Also, the communication technology does not exist to send pictures back than any existing radio telescope receiver could receive. It's just too far, and requires too many bits to send even the most rudimentary picture. For more on that, see my post on "Aliens watching 'I Love Lucy'".
Impressive proof the universe is safe from Lucy. Is the reverse true. Is SETI similarly hopeless? Or is there some alternative transmission method that theoretically could bridge such distances?