My experience agrees with your first statement, but more in the sense that really good thinking was possible when I was at a pace I felt confident I could maint

My experience agrees with your first statement, but more in the sense that really good thinking was possible when I was at a pace I felt confident I could maintain for an hour or two without being overly tired afterwards. Of course that pace increased over time and eventually my 'jog' pace was faster than my starting 'run' pace.