Does it speed up? No.

Does the story get significantly better once you're out of ARR and into HW? Yes.

Does the amount of combat-based content within the MSQ increase? Not really, though most of the later solo duties are more interesting than the early ones.

If you're looking for something more combat focused with less story detail, there are other games out there designed for that. This game is designed for those who like a story-based experience.

If you're enjoying this game other than MSQ, skip the cutscenes and just do whatever your quest objective says to do next. I've met players who do that so they can get to level cap and end game content as fast as possible. Most of them also regretted it because they didn't have a clue what was going on in the instanced content and ended up starting a new character from scratch.

It's okay not to like the game and quit playing if you feel like you're wasting your time. It's not going to be right for everyone, just as there are other games I've tried and no longer play because they're not right for me.