You can take a look at the New Horizons to get an idea of what a moderately capable trans-Neptunian probe costs today (~$700M). If you made several, economies o

You can take a look at the New Horizons to get an idea of what a moderately capable trans-Neptunian probe costs today (~$700M). If you made several, economies of scale would of course lower marginal costs somewhat. But the money isn’t even the main bottleneck (although it absolutely is a huge one) – power is. Specifically, the RTG radioisotope generators that are our only reasonable way of powering things at distances beyond Jupiter. Synthesis of radionuclides (eg. Pu-238) suitable for RTG use was originally a nice side effect of nuclear weapons production, but these days availability is very low even though the DOE recently restarted production after a long pause. In the 21st century NASA has launched exactly three RTG-powered missions: New Horizons (2006), Mars Science Laboratory/Curiosity (2012), and Mars 2020/Perseverance. The next will be the (very awesome) Dragonfly mission to Titan, planned to launch in 2027. So given a cadence of roughly seven years, and one out of four missions targeting trans-Neptunian space, you could expect to launch an interstellar probe every 30 years or so, barring significant advances in power technology. The next one will most likely be a sorely-needed Uranus or Neptune flyby mission that would possibly launch in the mid to late 2030s. There are maybe a dozen reasonable mission proposals submitted for every mission that actually ends up at the launch pad. The competition is fierce, and any proposal has to argue its return on investment incredibly convincingly to get selected for implementation. We now know many interesting Kuiper Belt objects that would definitely deserve a closer look – but we also know many other things that are much more accessible and would also deserve a closer look! No amount of extra money would realistically allow NASA (or any space agency) to fly missions simply "because we might discover something" because there are always many, many other mission proposals in the pipeline with vastly better justification than merely "because we might discover something".