While such an idea is fantasy IRL, it does confer obvious scif advantages like:
1. 1g travel to anywhere. Refueling? No longer necessary.
2. With sufficient thrust you can ship large payloads more efficiently. Basically you could totally end the maritime sea shipping industry, replacing it with air to orbit and powered thrust reentry shipping instead.
3. Obviously for that to work the exhaust, if there is any, must not leave cancer causing radiation behind, or else have no exhaust at all.
How To Prevent WMD: Two ways are kind of obvious.
1. Limit acceleration time by design. Sure the engine COULD accelerate forever.... but it has an inbuilt timer that will shut it off eventually. Kind of like how automobiles have governors that will automatically reduce speed if you hit maximum (100-120 mph).
2. If someone attempts to tamper with the timer the engine will be ejected from the ship and an inbuilt bomb near the engine will detonate. Destroying both the engine and the tamperer.
3. Only military or special science vessels would have true unlimited acceleration. As whoever ran them would have to be trusted.
Other points: Constant acceleration is NOT a panacea. At near light speed I read that radiation blue shifts into the X-ray range and will kill or burn up the ship over time anyway. Also at such high speed even dust particles in space are like TNT to the hull hitting it.
Also the Oort cloud is said to have some objects of likely asteroidal ice that are mountain size. They are scattered across vast distances (about 2 LY) but you would have difficulty dodging at that speed. Oort clouds are like the solar system's own whipple shield, a good chance every solar system has one too.
And here is a joke:
I think space dust, micrometeoroids and the like are one of those things that you either assume that your protagonists can deal with using available technology, or you assume that they luck out and don't get clobbered by a rock that's big enough to kill them. Or a mixture of the two - assume they can deal with dust particles and small rocks (and throw in an explanation of why if you like) but then assume they miss the big rocks.
Is this entirely satisfactory? Probably not if you're looking to create a very detailed and plausible setting, but it's a useful narrative convenience because 'death by space rock' is a really lame way to kill off a character.
"So what exactly did happen to the enemy flagship, Captain?"
"Uh - we picked up a short duration, high intensity radiation source on the edge of the Oort cloud, Admiral. As far as we can tell, they hit a magnitude eleven object on the way in. Feel a bit sorry for the blighters to tell the truth."
"At least it was quick."
"Aye, sir."
-From KSK
