Going faster means expending more energy. At some point it won't make economic sense to go faster, even if technically you could. Freeze dried wombs don't care whether the journey takes a thousand years or five hundred, but the costs are very different.
At the same time, you could send information, compressed, enough to accurately reconstitute the travelers in spacetime. That would take some raw materials and a plenty of energy. However, the required devices might be much more resilient to acceleration and radiation than any possible human body.
It takes the same amount of energy to accelerate at any speed in space. The limit is our determination really, it is possible to visit our nearby star with ~200 hydrogen bombs
No it doesn't. Your mass increases the faster you go, so that more and more energy needs to be expended to accelerate more. At 50% light speed, you're 15% heavier. At 90% light speed, you're 129% heavier. At 99% light speed, you're 608% heavier. Your mass goes to infinity as you approach the speed of light, which is why the speed of light is unattainable for objects that have mass.
