I would never ever read those logs and I wouldn’t install that keylogger, the situation that comes to my mind is … my child is missing from home for a few days and I am hoping he/she chatted with someone about it from her computer.
Yeah - this happens more than it should, but in nearly every instance, Law Enforcement can get as much information from the computer itself as they would if you added a keylogger.
There will always be cases where you can say “if only I had X it would be [easier|faster|better]” but that is a moving target.
If your child has a phone, for example, most of their chat will be on that (snapchat is the primary tool for most tweens/teens).
I’ve dealt with situations where the victim has had voice calls which would have led to a faster outcome - it would have been easier if they had been recorded.
It is always possible to think of a situation where your current surveillance is insufficient and you should have had more. But it is a path to insanity.
While there are genuine risks and threats in life, they are actually a lot less than we might perceive from media portrayals. The greatest threat, by a significant margin, to children comes from trusted family members. Grooming/abduction is much, much less likely.
Using the US as an example:
Around 350 children (under the age of 21!) are abducted by strangers each year (Kidnapped children make headlines, but abduction is rare in U.S. | Reuters).
This is out of about 80,000,000 people in that age range (Demographics of the United States - Wikipedia).
This generates a ballpark risk of abduction at about 1 in 230,000. Now that certainly isn’t zero but you have to ask if it is probable enough to justify the measures. Out of those 350 cases per year, my own belief (no stats here, sorry) is that the number of cases where a keylogger on the computer would have helped is probably fewer than 5. Lots are simply “snatch and grabs” or grooming via phone apps.
So, this boils down to a decision between the cost of installing the spyware (loss of trust, needing to disable other security controls, need to monitor, risk of capturing something which results in the device holding child porn, wiretap issues etc) is outweighed by the benefit (possibly finding something useful in a literal one-in-a-million situation).
At best you have a partial control which is in place to mitigate a very low probability risk for the short period of time until the child is able to own their own device. Then the control is gone.
You might be able to protect them until they are 18 (or leave home) but the risk to them remains pretty much throughout life. It is significantly better to trust them and teach them to be safe as this will continue to work when they are no longer being constantly watched by a parent.