It seems to me akin to asking if a doctor should take measures to control pain and inhibit infection while amputating a limb to treat a fracture. Well, yes, but is there a better way?
Reasons to question whether we should create Ministry M to advance Goal G might include:
• Ministry M will not have incentive to achieve G, and may even have incentive to not achieve G (thereby renewing or increasing its budget next year)
• Ministry M will not be as careful spending other people's money to achieve G as the people who want G would be if they spent their own money to achieve the goal, leading to waste
• Special interests which are directly affected by G will be highly motivated to influence Ministry M, while the funding for M will be collected so broadly that the unwitting and perhaps unwilling underwriters will not have adequate reason to object or even investigate
• Ministry M will attract a crowd of parasites and hangers-on who game the system and milk it for profit, the rent-seekers
The best way to avoid the rent-seeking is to simply refrain from providing opportunities to rent-seekers. For example, established car makers are fighting Tesla by getting sweetheart laws that require sales through dealers (which they already have and Tesla wants to avoid). And taxi companies are fighting Uber and Lyft by getting regulators to block the newcomers from providing the often-superior services their customers love. Why would you think it helpful to add another layer of regulation to reduce the harm of these harmful regulations? Just let the businesses duke it out and the customers will decide who they like best.