Nothing is impossible, but some things are improbable. - Old Vulcan proverb.
It's not that warp speed is impossible but faster than light travel is not probable.
Our main form of fuels we use are fossil fuels. If we expect to travel near light speed we need different ways of propulsion.
We do and have used Ion drives to move space vehicals but those are too slow to start up and way to hard to slow down. Ion drives work as following if you were to launch a ship toward Mars from Earth using an Ion drive, you could accelerate towards Mars up until a little before half way when you would have to start slowing down.
The "main" problem of space travel is not how to accelerate to a near light speed, but more how do you slow down from near light speed? Once you figure out how to slow down then it's all down hill from there.
Also, it's theorized that in space there would be too much "friction" from dark matter for a vehical to achieve near light speed.