Except the death rate for children by COVID is virtually non-existent -- in the 0 to 17 year age group it is 246 out of about 534,000 deaths and nearly every one of those children have had a significant underlying health issue. For 18 to 29 year old's it is 1957 out of 534,000 and again, many have had significant underlying health issues.
I have no children so this is probably easy for me to say, but I would not have them take this vaccine. At 64, it is a no brainer for me. At those young ages, not sure why risk it.
Your conclusion is logical. But I am not convinced that it will turn out to be a correct one in the long view. If the vaccine does turn out to be very safe, (Other than the rare allergic response which can happen with any foreign substance we inject or ingest), then it would be worth considering vaccination of everyone, as we do with smallpox, measles, mumps, chickenpox etc. The object being to remove this virus (or current form of it) from exposure to the whole world population. Smallpox for example is literally gone, except for keeping a small amount in very secure labs in case it is needed in the future for some reason. Actually, the vaccine for smallpox was and is made from Cowpox virus. We are not susceptible to Cowpox, but we do get full immunity to Smallpox from it.
So if the vaccine is safe, which I trust it will be concluded, it may be worth considering giving it to younger children as well in the future. Even tho they usually don't die or get very sick from this virus, they are still capable of carrying and incubating it to levels that can be contagious to grandma and gramps, who are often involved in their care, and to those with impaired health as well. Meanwhile the hysteria (unfounded) that vaccination in general is not good for our kids is misguided IMO. If not for vaccinations, many of the people you know would not have made it to adulthood. And reaching 90+ years would be a rarity instead of common as it is now. So for now, being cautious may be wise, but in the future, who knows? Also, if the vaccine is safe as it appears to be, the risk to young children of taking it, still appears to be less than the risk of getting the disease. That one rare susceptible child if vaccinated may be here to enjoy his 90th birthday (perhaps if he dodges life's other risks).