How do you propose to power that acceleration as it becomes ever more energy inefficient?
Oh its a staggering amount, even with fusion as an option you are likely talking like 50,000 tons of fuel if your sending a "real spaceship" out there.
Now is that a captain insano level of fuel?....it is. Is it beyond the realm of possibility....its not.
Again we can't look at today's technology and say how would you do this. The answer is...you don't. But we can make some realistic assumptions about future tech that could do the job.
1) Delivering fusion power at reasonable energy.
2) Industrial food creation. Aka producing food from energy + base materials rather than agriculture. The notion of growing your own food in space is a dated concept, we will make food an industrial process, and therefore much more space/energy efficient.
3) Next gen materials. We are already going through a material revolution right now both with AI assistance and simply that:
a) We have learned the fundamentals of how atomic structrure = material properties. We are no longer fumbling in the dark, we basically have an instruction manual.
b) Insane material "printing" capabilities. We have the ability to print materials at the atomic scale, creating a level of precision underheard of before.
So with that in mind, when people are discussing "how can we possibly have ships that aren't cooked by radition or could withstand dust moving at near relativistic speeds.....give it 20-40 more years. We are going to have materials that make our strongest stuff today look like toilet paper.