You'd need to convert approximately 100,000x the mass of your capsule to energy to reach that kind of velocity, and the same again to slow back down at the other end. So for a one way trip, the payload would be on the order of 1/1,000,000,000,000th of the mass of the ship.
For comparrison, that means a starship the size of a Saturn V would be able to deliver a 3 milligram payload. If you assume even very slight efficiency losses, the possible payload size collapses quickly. Remember, some of that payload would need to be taken up by the propulsion system.
The problem with picking up reaction mass along the way is, you need to lose energy to accelerate it up to your own current speed first before you can consume it as reaction mass to speed yourself up. As you get closer to lightspeed, even with perfect, lossless conversion, e.g. at 0.9c you lose 90% of the energy of the reaction mass bringing it up to your own velocity and get only 10% of it for beneficial thrust. The total of required reaction mass, which was already ludicrously huge for any practical payload, balloons massively.
If you do actualy have energy conversion losses, those limit your maximum possible speed. If you lose e.g. 1% of the energy you convert, then once you're at 99% lightspeed, the energy you gain from burning the reaction mass is the same as the energy you expended bringing it upto your own velocity. So there's no net gain.
A top speed of 0.99C only gives you a time dilation factor of about x2.3 or so.
And of course all of that is assuming magic fantasy tech with unbelievably high efficiencies and negligibly sized engines and mass storage.
Or alternatively instead of placing stationary fuel pellets in your flight path, have them accelerated by an external accelerator to as high a speed as possible.
Light years is a measure of distance not time. As a result 10,000 light years measured from either parties perspective is 10,000 light years. ie a human on the ship would still experience 10,000 years of travel. No human can currently live that long.
Now change your hypothetical numbers to 10 light years and you're not misunderstanding anything. The human aboard the ship would have experienced 10 years of travel. However, any observer from Earth would have experienced 10*(some large factor) years, such that making a return trip "home" is impossible.
There is no way to live longer by traveling fast.
It's my weak understanding that because of time dilation & length contraction I could climb aboard a sufficiently powerful ship and travel 10,000 light years before dieing of old age. But, when I got there, I would find that 10,000+ years had passed at the destination while they waited for me. And, that if I made a return trip, Earth would be 20,000+ years older. But, importantly, /I/ would not necessarily be 20,000 years older.
So, the speed of light still sucks, but it mainly sucks if you care about returning home. If you give up on that goal, relativity does not say it's impossible to travel to arbitrarily far locations in human-scale timeframes.
Am I misunderstanding?