Also once you have created the infrastructure of hundreds or thousands of very powerful lasers to accelerate the tiny probes to incredibel speeds, sending many probes instead of a few doesn't add much to the cost anyway.
The Voyager can be overtaken in several years if we to launch today a probe with nuclear reactor powered ionic thruster - all the existing today tech - which can get to 100-200km/s in 2-3 stages (and if we stretch the technology a bit into tomorrow, we can get 10x that).
I was listening to an old edition of the Fraser Cain weekly question/answer podcast earlier where he described this exact thing. I think he said that someone has run the numbers in the context of human survivable travel to nearby stars and on how long we should wait and the conclusion was that we should wait about 600 years.
Any craft for human transport to a nearby star system that we launch within the next 600 years will probably be overtaken before arrival at the target star system by ships launched after them.
Because the alternative is everyone waiting on one big 600-year government project. Hard to imagine that going well. (And it has to be government, because no private company could raise funds with its potential payback centuries after the investors die. For that matter, I can't see a democratic government selling that to taxpayers for 150 straight election cycles either.)
And the research doesn't need to be anywhere near continuous. It's valid to progress though bursts here and there every couple decades.
And a lot of what we want is generic materials science.
Btw 500 AU is 69 light hours.