Probably more likely that we work out how to fold spacetime than we get there in anything like a high enough percentage of the speed of light - the fastest object we ever made travelled at something like ~0.064% * C so we are looking at ~750 years with current technology and presumably we'd need to switch on the probe in 3/4 of a millennium and figure out how to slow it down and get it into some sort of orbit around the planet.
750 years is hard for me to get excited about even as a vampire.
With variations on nuclear propulsion we could plausibly get to up to around 12% the speed of light. At least that's the number quoted for Project Daedalus [1], which is using nuclear fusion for the first stage and nuclear-powered ion engines for the second stage. With the cruder but more realistically achievable right now Project Orion design (riding the shockwaves of nuclear bombs) you could still get to ~3% the speed of light
But even at 0.12c, we are looking at 400 years to get there. And we'd be zooming by at 12% the speed of light. If we want to slow down a bit that'd add hundreds of billions to the cost.
It might be worth waiting another century to see if we can come up with a faster design in that time. Not like closer targets like Alpha Centauri, where the thing stopping us is mostly just the absurd cost
Adding to this:
Those 190km/s of the Parker solar probe were, crucially, periapsis speed.
This is a bit like bouncing a rubber ball from a building, measuring its speed at ground level and then going: "Given our fastest achieved speed, we expect to hit the cloud level in <10s".
~200km/s sustained speed is already insanely optimistic for anything we could realistically build in the next half century, so your position is even more ironclad than it looks at first glance.
Universe #23: keep solar systems far enough that they can't make war on each other.
We are looking at 75,000 years. You forgot the %.
Honestly a near millennia long expedition would be very cool, and doesn’t seem too long on the scale of space stuff.
It’s highly unlikely we’re ever getting FTL. We should become comfortable with that and let go our fantasies. Let theoretical physicists chug away at this, we should get underway with projects that are possible with known science.