STAT recently had a very good article describing the pros and cons of an mRNA vaccine. But I don’t think this con should be underestimated (boldface mine):
When mRNA Covid vaccines became available in the winter and spring of 2021, people started swapping side effect stories. Some felt nothing, or reported at most a bit of a sore arm. Some spiked high fevers, experienced chills, aches, malaise — symptoms that approximate the experience of having the flu — for a day or two. Some get knocked flat every time they get an mRNA shot.
“I don’t react,” said Arnold Monto, an influenza epidemiologist at University of Michigan School of Public Health. “My daughter … knows she can’t be doing any normal activities for about 48 hours.”
Traditional flu shots are not associated with the side effects that mRNA shots have become known for.
That reputation for reactogenicity, as the the likelihood of unpleasant side effects is called, will probably turn some people off of the idea of mRNA flu shots, said Ben Cowling, chair of epidemiology at Hong Kong University’s School of Public Health. “With the reactogenicity profile, with the likely cost, I’m not sure what the uptake would be.”
While egg-based vaccines have flaws (if nothing else, the vaccine antigen evolves in the egg), I really don’t want to get knocked flat on my ass for two to three days to get a flu shot, especially when it seems to work fine for me*. I would like to see a ‘Novavax style’ version, because that would allow a delay in deciding which influenza strains to cover (that’s a good thing, since we’re less likely to include a strain that isn’t important) and there also isn’t the within-egg evolution issue. But I think mRNA flu vaccines will get less uptake, in part because some people don’t want to take that much time off, well, from living (or need to work etc.).
Hopefully, mRNA influenza vaccines will be one of multiple strategies.
*To the best of my knowledge I have never had influenza (and for as long as I can remember, I’ve been vaccinated every year). If I have had influenza, the vaccine provided enough protection such that the infection only resembled a cold. In fact, the only time I’ve ever had ‘flu-like’ symptoms was after COVID vaccination–though given the small, but non-negligible, chance of long-term or critical health issues from COVID, as well as the protection it provides to other people by reducing transmission, the mRNA COVID vaccine is worth getting, even with side effects.

I guess I’m one of those lucky ones who never got notable side effects from the mRNA vax. A sore arm and some very mild funk for the rest of the day is the worst they’ve done to me.
It does seem obvious that we should have options for folks who tolerate one or the other better, though.