Simply put, it makes logs unreadable for humans without tooling. Things primarily touched by humans should be as friendly as possible to them. Prior to the advent of structured logging, every log message had a unique visual 'fingerprint' that the eyes and brain could grok at a glance, and spot anomalies really quickly. With structured logs, everything looks the same and so you can't use the brain's inbuilt abilities to process them.
And if you did want tooling to help, then typically the formats were regular and so you could use ordinary text processing tools to help. sed, awk, grep. With structured logging putting everything into nested balanced expressions, you need parsing. Parsing works until you run across something the parser can't figure out. Say you have some Go code with a JSON logger object you're passing around. What if you want to log something but your logging object isn't passed to that function. (you could pass it everywhere but that increases the arity of every single method by 1, and are also reinventing global state poorly) You're SOL, now you're stuck with fmt.Println() and you just broke jq. No, jq does not handle this failure mode. No, Golang does not let you just spit out arbitrary JSON. Thy must use the logging object.
The only thing it helps is ingestion into databases for heavy machine processing. Which is fine, but don't make it the only or even default way software tools spit out logs. In every other way, introducing parsing into your workflow just slows it all down. The only way I can see structured logging making anyone's job easier is if they never understood how it all worked before.