The long incubation period and asymptomatic carriers makes for easy spread of the virus. It's hospitalization rate means a wide spread will literally shut down hospitals in whole regions. At current infection rates we're seeing hospitals being overwhelmed at regional levels.
Even if vaccines had been delivered after a Phase 1 trial of "no one died immediately" in the trial group, we wouldn't have enough vaccinated people to avoid social mitigation. We'd be in a similar situation as we're in right now.
It will take something like 75% of the population to be immune (by vaccine or previous infection) to have effective herd immunity. Even if vaccines had started distributing months ago it would still be a long time before we hit that 75%. Distributing vaccines after the phase 1 trials might ultimately get an immune population to that 75% sooner but it wouldn't stop any of the damage happening until that number is reached.
Even if no one died from COVID the "long hauler" after effects can be crippling. Some 10-20% of COVID patients end up "long haulers". If the virus were to spread to significant portions of the population because no one practiced social spread mitigation because they assumed the vaccine would fix everything you're still in a terrible situation.