Your first point: That shouldn’t matter. Havenport should be capable of seeing the big picture. He should also know that getting a unique and valuable regiment killed off isn’t good for his reputation or Tierra’s military situation as a whole.
Your second point: They aren’t useless. They use carbines, which are more accurate than muskets, so if you put them on the wall they can get lots of kills. Outside of direct battle, they can be used to go on patrols or hunt partisans. Also, do keep in mind that the more prestigious cavalry units are with the King, so chances are the Dragoons are the best cavalry force he has on hand.
Your third point: No, you send those guys in first. That’s what Havenport did with the Highlanders. Then you send the quick and accurate sharpshooters to reinforce them, guard their flanks, provide cover fire, and perform non-combat tasks (guiding reinforcements) so Marcus doesn’t have to worry about them and can commit his command entirely to direct fighting, which is what the Highlanders excel at.
Speaking of Lord Marcus, also remember that Havenport is sending you in to reinforce his brother and his own regiment (which consists entirely of pre-trained soldiers who are loyal to his clan, so if it gets slaughtered that means he has less manpower to keep the rival clans in line back home.) If he thought the Dragoons weren’t up to the task, then why would he risk his brother, his regiment, and his duchy’s security just to give them a position they weren’t even well-suited for to begin with?