glutathione is a steroid or not Glutathione: Master Antioxidant, Reducing Oxidative Stress, and Detoxification Glutathione deficiency induces epigenetic alterations

Shooting directly onto the peptide can create foam and mechanically stress the protein structure

Further, NICE and the BNF says that if there are neurological symptoms present, then every other day injections are the recommended treatment, so all the points you make about B12 being stored and sufficient are not really relevant

Science 347 , 771775 (2015)

Glutathione and Detoxification The role of glutathione in your bodys detoxification system is vital

Dounousi E, Papavasiliou E, Makedou A, Ioannou K, Katopodis KP, Tselepis A, et al

The augmented proliferative activity is concomitant with heightened vulnerability to superficial skin infections and tissue injury (Farkas and Kemeny 2013)