Having said that: there is the issue of cellular immunity. This is created in mucous membranes like nose, throat, lungs. Nasal passages.

These T- cells do kill the virus; thus, they prevent infection and blocks transmission as well. https://www.sciencedirect.com/science/article/pii/B978032339...

[..] The mucosal surfaces represent the major site of entry of many pathogens, and major challenges in vaccine development include safety and stability in a suitable dosage form. Micro- and nanocarrier-based delivery systems as nasal vaccines induce humoral, cellular, and mucosal immunity. The nasal route of vaccination could also offer immunity at several distant mucosal sites (oral, rectal, vaginal, and pulmonary), which is considered a simplified and cost-effective mode of vaccination with enhanced patient compliance. Most of the nasal vaccine delivery systems in the form of microparticulates, nanoparticulates, and liposomes are currently under development and prove to offer immunity in animal models. [..]

Vaccines injected into the arm bypass this mechanism. Nasal vaccine given by a liquid injected into the nose — duplicating the route that the virus itself takes. The problem is cellular immunity is harder and more expensive to measure. This could be the reason companies do not consider this method.