I would expect that the probe makers would want some benefits from the fleet of probes they sent, the only benefit I can think of to be had are information about far away objects, which is of scientific value. The probe’s makers will therefor have to keep contact with an ever expanding fleet of probes and sift through an exponentially increasing amount of information for millions of years. This just does not seem practical when you can just build a telescope. Now time may not pass that slowly from the perspective of the probe, but for the civilization on the homeworld, this method is painfully slow. They could have built thousands or millions of telescopes during that time to gather the same information (albeit of lower quality). Which is why you would probably want to probe your nearest neighboring solar systems, but nothing farther.
As for the moral reasons to not send out a fleet of self replicating probes. These are an extreme pollution hazard. An ever expanding fleet of robots traveling across the galaxy over millions of years, growing in numbers exponentially, exploiting resources in foreign worlds, with nothing to stop them if something happens to their makers. Over millions of years these things would be everywhere, and—in the best case—be a huge nuisance, but at worse they would be a risk to the public safety of the worlds they travel to. With these risks I believe a sufficiently advanced civilization would just build telescopes for their exploration needs.