As long as it doesn't mutate too much it should be doable.
I get the flu vaccine every year as a dose of flu (apart from being unwanted - I was really ill with it when I was healthy in my 20s) could cause a lot of damage if I have a relapse plus I have asthma and pneumonia was no fun either. Every year they take the four strains they think will be most prevalent in flu season. Sometimes they get it wrong but mostly, luckily for many, they get it right.
I think we're a long way off a cold vaccine simply as there are so many strains in circulation.
My grandmother was a nurse during the Spanish flu and was one of the survivors who had it but didn't die. I would sit for hours and listen to her tales about her nursing days and how they coped with the war. Lockdown now is different. I don't know how people now would have coped with real food shortages and the terror of nightly bombings, never knowing if they'd be alive in the morning. The men fighting KNEW they would be lucky to come home after each and every battle and that many would not be coming home to loved ones but still went. My father was in the RAF where he lost 75% of his team after one fight.
I do wish schools would teach history from the last 150 years to cover the history of diseases and vaccines, the discovery and widespread use of disinfectants and the importance of cleanliness. How important antibiotics are and that prior to their discovery a scratch could kill you and that gangrene was normal and feared. That "mild" childhood diseases can and often did kill and disable. It's amazing how much has been forgotten since I was a teen.
Home economics needs to be taught, too. Kids these days - and many of their parents - would starve if their food didn't arrive in a bag or with a ding. A year of basic cooking and hygiene should be a skill taught as many parents can't or won't. It's not helping the health of future generations.
Sorry, I'm ranty again. Just been reading about the Belgium GP who started the current round of stupidity with his unfounded comments about 5G and Covid-19. A GP!