Yes it is true that the vast majority of people who enter races are not doing it to be competitive. Timing implies competition (competition with others: my time was faster than your time. competition with oneself: I beat my time from last year. competition with the course and distance: I ran the hilly 10k only a minute slower that the flat 10k).
Races have realized that timing people accurately requires time and effort, and normally a fee to pay a pro timing company. Since most people are not running competitively they do not care about time and the race can save a lot of hassle by not timing them.
A clue might be found in the title of the event. If the event has "race" in its title, it might be competitive. If it is billed as a "run" or just a distance (i.e. "10k") it might not be a competitive event.
The truth is that this is what running has become. Most people, especially adults, do not race. They did not race in high school, college or anywhere. Some believe competition is bad. They do not care about the time it takes them to finish a given distance.
This is why there is very little correlation between the popularity of competitive running as a spectator sport and the explosion in participation in road runs. It is difficult for most people who participate in road running events to understand competition, world records, personal records, etc.
Viewing a race on TV is like viewing a completely different activity than what they do or why they attend something like the "Run for the Zoo" or a similar event. Time means little to them.
After 50 years of competitive running I rarely enter races anymore. I do not want or need the crowds, junky give aways, social scene, etc. And because I am old and slow and my times are poor, I have no need to put up with all that to pay someone to time me.
But I have nothing against the hobby jogger types that participate and do not want to be timed. They could be doing much worse things.