Why should I get a massage?

In the Galdin Quay restaurant, there is a spa in the back right that allows you to get a massage. Ignis pointed it out and hinted towards getting one, so I tried it out to see what happened. Noctis however did not appear to like it and bolted from the bed.

Why should I get a massage? What purpose does it serve?

There really is no purpose to getting a massage in Galdin Quay. In fact, the fact that you can even get a massage is listed as trivia in some places. From the Galdin Quay wikia page:

If the player speaks to the masseuse Noctis can get a massage. If the player reads the sign for the spa, his party members suggest they should do it but Noctis will decline.

And from the IGN walkthrough for The Errand Prince:

You can stop in the Galdin Quay outpost itself for food and lodging if you wish - or just talk to the waitress to learn more about the area. Everything here is probably a bit expensive for your level (though you can try for a back massage - even if Noctis isn’t keen on them).

It seems that this scene is merely added for humor, however, it's noted in this thread that Prompto will take a picture of the occasion, so that seems to be the one thing that will come from it.

Prompto will even take a pic of it too.

It's not a functional part of the game in any sense so nothing comes of making Noctis get a massage at any time of day or night.

However it's widely believed that the prompt to get a massage is to cue up some of the traditional odd-ball humor / programmer humor (hotdog shortage and "long cat" in FF8, as a brief example) though I can't see a programmer joke in that particular instance.

Perhaps it's just a way to illustrate a degree of humanity - the guy spends the whole game getting knocked around by monsters and can't handle a massage.