But that gets to what the Epstein drive basically is, in-universe: a 100% efficient fusion drive. No physical laws being broken, technically, just the nuclear rocket equivalent of a perpetual motion machine.

They do in fact go around at 1G (or 1/3 G) thrust for months at a time in the books and show, accelerating full speed for half the trip, then turn around and decelerate for the other half, for trips to/from the outer solar system. In the inner solar system it's only a few days to weeks to get anywhere. This lets them operate in artificial gravity without spinning the spacecraft, which is convenient for filming (although it's in the source novels too).

EDIT: Well, I should say that the propellant mass/delta-v is really high and that most of the fusion energy will can end up as kinetic energy of the propellant and ship. But the vast majority of that kinetic energy will be the propellant rather than the ship. To maximize ship kinetic energy over fuel energy you want the propellant to exit the ship at the same velocity the ship is traveling which is very far from what you see in an Epstein drive. But fusion provides tons of energy so that isn't going to be a figure of merit we care about.

Re: accelerating for many months at 1G is definitely bad physics, not only are you relativistic, you start getting into the kind of speeds where a minor meteorites will wipeout your ship. 1 gram meteorite with a relative velocity of 0.5c has 1.4e13 J of kinetic energy = 3.5 kton of TNT, so a small nuke.