An unprepared Andromedan ship was torn to pieces in "By Any Other Name", but the pieces were thrown inward
into the Milky Way...
It's quite possible that the Barrier exerts forces on all objects, or at least all warp coils, but apparently those don't have a single easily recognizable direction. Sure, we could argue that getting out is difficult and getting in is destructive but easy, but even that model is confused by "Is There In Truth No Beauty?" where a ship entering the Barrier is unable to get out either with or without engine power.
Of course, "Is There" features a slightly different shade of treknobabble from the rest of the Barrier episodes: the ship is said to have ended relatively far outside the Milky Way (and supposedly well beyond the Barrier), and entered a "spacetime continuum" where warp navigation is impossible for some reason. Or possibly the "continuum" briefly confused inertial navigation and then went away, and Spock is saying it will come back if they try to re-engage warp.
The act of going through the Barrier is mentioned separately and, in synch with "Where No Man", is stated to require warp power because impulse engines won't suffice. Or, more accurately, sublight speed doesn't suffice, possibly indicating that the Barrier is so thick that sublight travel would take forever and/or expose the ship and the crew to dangers for too long. If the latter interpretation is taken, then there's no problem for the Valiant
's engines in the act of going through the Barrier from outside in (the storm took care of the other direction), but a slow passage would increase the odds of divine emergence...