Some of those bodies in the solar system no longer exist. Imagine if you could travel way faster than light. And picked one of those points of light and headed toward it. It is possible that somewhere along the way that light would just cease to exist before you ever got to it. You turn around and head back toward earth. And it would re-appear.
If humans had FTL we would go to the closest ones first those would not be millions of light years it would be hundreds and stellar lifespan is measured in millions and billions of years. We would know how far along a star is in lifespan by it’s spectral lines. Even a million light years distance is well within stellar lifespans of sun sized stars.
The bigger problem is the universe is expanding and stellar drift in orbits under gravity and dark energy / matter not fully understood. If we have FTL like Star Trek then you need absolutely clear paths for the folding of space in front of the ship any gravity well or stellar/planetary mass would be shredded by a Star Trek warp drive. Same for jump FTL like Battlestar Galactica which jumps from one place to another via sub space, so again no gravity well or masses at the exit point or you jump into a star or planet or asteroid field. Stargate style hyperdrives also use dimensional twindows to leave relative law space and open an exit dimensional window which again must not be in a gravity well or some planets mass.
Exotic theories such as quantum tunnels, micro wormholes all require exotic energy and some means of deconstructing matter into particles that fit down the quantum tunnel or micron sized worm hole event horizon. This is how the Stargate is supposed to work in that show it’s a wormhole at each end with thrle gates doing the decon and recon of the matter streams.
The only one grounded in any real physics is the space folding warp and you would need black hole levels of energy or dark matter and dark energy the universe expanding kind.
At relativistic speeds you are only getting to stars close enough that you can see how deep into their billon plus year long lifespans they are and a 20,000 year trip is a tiny fraction of that time.