There's also the fact that the faster you are going the more time dilates, if we aren't using FTL. If you're going .99999c you'll get somewhere much faster (from your point of view) than if you are going .9c. The rest of the universe will still pass time as normal and Earth would be a few million years in the future by the time you got to Alpha Centauri and back, but for you it could be down to days or hours.
Wait... isn't Alpha Centauri like 4 and a half lightyears from the Sun? Even at half the speed of light, it would take you less than 3 years to get there. At .99999c it'll take you just nearly the same amount of years than light. It's just that, from the POV of the traveller, you keep going faster and faster even if the "c" number isn't really going up. So, for outsiders, you just went 0.0001 faster, to you it might seem twice as fast.
That means you feel like you arrived in a week, or a day, or even a fraction of a second, while you took "real" time to get there from our perspective (so we all aged 4.something years or so, you didn't). Definitely not millions of years...
Basically, you're spending more energy/fuel to get there faster, but only relative to your POV, for all of us, it's just a waste
(if it takes millions of years in the first place {what, are you
driving there?
}, you are going nowhere near the speed of light, so relativity barely applies to POVs... so you'll be dust by the time you get there
)