so this image gave me time to think about teleportation machines.
I do think that travelling arbitrarily close to the speed of light (i.e. practically instant) might be doable, and probably actually is, but it would be so expensive that nobody would use it anyways.
i mean, you can just build a rocket and accelerate it arbitrarily close to the speed of light, using enough fuel. but the cost of doing so is prohibitively expensive, so there's no practical way to actually ever do that in practice.
slow travel is just much more economical, that's why teleportation is out of the question. but that's economical reasons, not a fundamentally physical one.
this comic argues that through teleportation machines, travel would become instant and cheap. and i think it's the opposite: the faster, the more expensive.
teleportation machines probably work by accelerating every part of you to the speed of light and slowing them down again on the other side. so it really is like a rocket acceleration.
and no, they wouldn't kill you any more than stepping on an airplane does.
there's also this existential comics about it that argues:
but that's already the case on an airplane. if you drink a cup of water on the airplane, the atoms inside your body get swapped out for new ones; that literally happens all the time. so it partially kills you? but nobody thinks that way. (ship of theseus)
I think the chart you posted helps prove my point. Mass go up, energy needed exponentially go up. That doesn't just mean "more fuel", it means more power behind the thrusters. And that chart isn't even taking into consideration the gain of mass as you increase in velocity, just the mass of the vessel itself.
As you approach the speed of light, the amount of light that reaches these sails decreases, making them less effective, while mass is still increasing.