... who sometimes likes to pursue knowledge for the pure sake of
learning something new about the Cosmos. If it also happens to
make our floors shinier and our teeth whiter, then bonus for the
human race.

I would be all for adding some instruments aboard a Pioneer
Anomaly probe that would investigate deep space and any worlds
it may pass by for a gravity assist to add to the scientific bonus.

As for cost, I hope someday to see not one or two big machines
costing billions being flung out into space and if they have an
accident the whole mission is lost, but rather many smaller and
more capable probes that can cover many areas at once. If a
few are lost, it is unfortunate but not the end of the game.
Nature has been doing this for ages with plants and animals
spreading their seeds into the world.

As for what else can be gained from investigating this anomaly,
the fact that we still know so little about it could mean there
is something unexpected out there that might affect all future
such probes, or perhaps there is a phenomenon or set of objects
that could provide benefits to future humanity we cannot even
conceive of right now - even though part of me reviles at the
arrogant idea that everything in existence is supposed to benefit
us in some way.