I don't think so since none of those vaccines we get as kids are only good for a season, and with limited effectiveness. I think that's the real reason, not marketing.
Perhaps? Languages and common vernacular evolve in surprising ways.
The use of 'shot' was originally meant to indicate that it is given via injection; however the word 'vaccine' may have become less common because rapid mutations result in new flu vaccine versions twice a year, and vaccination only gives a limited time resistance. It would make sense this would leads to a less formal vernacular.
Since orally administered flu vaccines are in clinical trials, we might get to see vernacular evolve to accommodate them soon.
All that said, "flu shot" is a common name for influenza vaccines. There is no requirement that a vaccine be highly effective or impart a long-term resistance. Rather, vaccines which are not safe and measurably effective are not desirable and thus tend to not be made available.
