Luigi also knows Mario is an absolute quack. Look at how his medicine is shown to work. He uses gigantic viral cells in a contained environment and they only clear out if the color matches. They only work in the perfect, unrealistic environment.

Outside of that, he literally throws those giant pills at people. He's not a doctor, he stole that entire outfit from a Spirit Halloween and began randomly assaulting people claiming them to be his "patients" and because of his connections with Peach, they let him pass.

Luigi is tired of this nepotistic bullshit all across the Mushroom Kingdom, and knows what needs to be done.