It is used in photodynamic therapy to selectively kill some viruses (see below) / bacteria (e.g. mycoplasma) [2].
When entering the bloodstream, it binds selectively to the nucleus of the viruses it is effective against. It's the same mechanism why it's effective as a dye to stain microbes under microscope. Methylene blue best absorbs light at 660nm wavelength, which at the same time penetrates into human tissues deeply. When light is absorbed, methylene blue disintegrates to harmless molecules while releasing reactive oxygene species, killing the virus.
It is a very safe drug, so the same logic that bsaul mentioned could be applied, and therefore would be a responsible move. It is also beneficial to mitochondria and effective against fungus.
[1] https://europepmc.org/article/cba/518857 [2] https://www.sciencedirect.com/science/article/abs/pii/S15721...