So let's say that there are a thousand people who want to run that 5K. If one person starts every minute, people are going to be running from 7 AM until midnight. How is that going to work? If the interval between runners decreases much further, you're just going to end up with crowds like before (albeit smaller).
Local government and the event's liability insurance carrier will dictate how many people can race.
Races need permits, road closures, police traffic control, and the like. It is the local authorities that will cap entries and RDs will have to live by those rules to get their events approved. If your city says that gatherings must be limited to 1000 people or less, then that is the number you will have to work with. In a race of that size, then the RD can stagger fields as such for a 5K:
Runners only, no walkers permitted to enter - 1000 entrants
8:00AM - Wave 1: Sub 21 minute OPEN MEN (30)
8:10AM - Wave 2: Sub 25 minute OPEN WOMEN (30)
8:20AM - Wave 3: Sub 27 minute MASTERS MEN (45)
8:30AM - Wave 4: Sub 32 minute MASTERS WOMEN (45)
8:45AM - Wave 5: 21- 27 minute MEN (175)
9:00AM - Wave 6: 25- 32 minute WOMEN (175)
9:15AM - Wave 7: 28-40 minute MEN (250)
9:30AM - Wave 8: 33-45 minute WOMEN (250)
Those numbers will fit within the allowable crowd sizes that other nations have been mandating and having success with. The time spaces between waves will allow the air to clear after each group. Participants will be expected to wear masks if mandated per local guidelines. Like track meets, at final call, be stripped down and ready to race. Race officials will marshal the wave to the starting line and the gun gets fired pretty much immediately.
This is also predicated on the assumption that insurance carriers will write policies protecting the organizers from liability claims related to COVID-19. Larger events such as marathons may also require entrants to be current USATF (or corresponding foreign federation members) to further spread the liability shield. No insurance? Then your event isn't happening.
Even in the pre-COVID world, you could not simply hold a race on public thoroughfares without civic blessing, support, and legal protections. COVID now complicates that equation.