In the US, the variants of flu chosen for the production of conventional influenza vaccine are determined from what is observed in Australia and New Zealand around this time of year. Then those are produced (which takes six months or so). 

Orders by vaccine producing companies are taken in April, for delivery by September. 

What most people fail to understand is that influenza, like COVID and many other respiratory pathogens, are RNA viruses. RNA viruses will evolve and adapt much more quickly than DNA viruses, such as smallpox, cowpox, camelpox, monkeypox. This is one of the two reasons why we've been able to eradicate smallpox: the smallpox virus is in the family of "orthopox" viruses, it doesn't change much (over many, many years), and these viruses confer sterilizing immunity[*], which influenza (and influenza vaccines) do not.  Since you're familiar with the concept, think of DNA viruses slowing genetic drift by having a "checksum" - ie, the second strand on the helix "checksums" the other strand. This second strand is missing in RNA viruses, so genetic drift happens much more rapidly (again, look at how quickly COVID developed variants). 

The flu vaccine helps reduce the severity of the disease, but it does not eliminate the risk, nor does it give sterilizing immunity (ie, you can still be asymptomatic and transmit the flu). 

mRNA based vaccines, as we currently have them, aren't about to change the speed at which RNA viruses can evolve, nor are they about to make the underlying viruses confer sterilizing immunity. So while they might be more effective at preventing you from getting the virus for which they are designed, they're not about to solve the larger problem. Public Health bureaucrats need to stop living on the reputation of the smallpox vaccine, and start educate the public on the differences between RNA and DNA viruses, and what is sterilizing immunity and why most vaccines do not confer sterilizing immunity because the underlying virus doesn't do so either.

[*] Sterilizing immunity means that, once you have had the particular virus in question (eg, smallpox), and you survive, you can never, ever get smallpox again, and you can never be a asymptomatic carrier of the disease. Sterilizing immunity means you're "one and done" for life. The smallpox virus killed about 30% of anyone who caught it, but if you survived, you were done with smallpox for life. Likewise, the vaccines for smallpox confer sterilizing immunity, because the vaccines are based on less-serious orthopox viruses. eg, Jenner used cowpox for his vaccinations. The modern "monkeypox vaccine" is actually a smallpox vaccine, designed to replace the ACAM 2000 vaccine which was so despised by those who got it.