The duke's reason isn't just valid, it's practically required. While I didn't take their expiration in account, I thought that mean they can't build more locomotives without Miyabi. That's bad already, but on public infrastructure, it's obviously lethal. If any government spend public money on project that can't last long enough to justify them, then it's corruption.
IMO, it's already an unspoken requirement the moment this project was designated a public project. The duke probably expected it to gone without saying, as it's. But Miyabi probably didn't expect it, as well as the public project status.
You can argue about short-term economic boom, but for country, it's long-term that matter the most. And short burst could be harmful in long run if it's not capitalized proper. It's a recession in making, and we know recession breeds contempt.
But what about the tunnel? One of my doubts on this project is that, it's opening a path to the capital. That means more vulnerable point to defend. If he build the tunnel without permission, it'll be a treason, almost certainly.
And he need permission. It's feudal era. Land belongs to landowners, aka, nobles. If you dig tunnel under a private land without permission, getting sued is practically guaranteed, with exceptions of the cases where you getting killed first.
Yes, Miyabi could, and should, ask for prototype expense, but permission withholding is a right thing to do.