The barrier still looks like a relatively thin band that they could have gone over or under
Remember Kirk's own words here:
Kirk: "Other vessels will be heading out here someday and they'll have to know what they'll be facing."
No matter what the shape of the Barrier, Kirk
deliberately flew into it.
True, his supposed mission was to get outside the galaxy, and we might think he would sidestep these sorts of obstacles so as not to jeopardize his primary goals. But then again, we have no reason to think that the Barrier came as a surprise to Kirk and his crew. As many have argued, in the Trek universe it ought to be visible from a long distance away, and familiar to our heroes for that reason already. The original mission profile may well have been to fly deliberately to this well-known but rarely approached Barrier, test it, go a short distance beyond it, and then return.
I mean, it's not as if there were much to explore
beyond the barrier as such. Not with the resources of a standard 23rd century starship as these are later defined to us, at any rate. I realize this wasn't a concern for the original writers, but we're discussing the greater Trek context here anyway. In that context, a mission to challenge the Barrier makes sense. A mission to get to Andromeda, or the Magellanic Clouds, does not.
Timo Saloniemi