First off, you need to step into an actual PICU and see for yourself. The reality is the exactly opposite. The degree of autonomy depends on whether the unit is closed or open. I'm sure the PICU attendings and fellows on this board will add their 2 cents about the matter of open vs. closed, as I only have the perspective of my institution. Regardless, the large majority of sick pediatric patients fall under the care of the pediatric critical care attending and not the pediatric surgeon. Common medical cases you may see in the PICU include bronchiolitis, asthma, septic shock, croup, HUS, kawasaki shock syndrome, GBS, overdose (of everything scary), pneumonia, TBI, hypoxic brain injury from NAT, botulism, status epilepticus, severe anemia, oncology pts with complications, ARDS, CHD in cardiopulmonary overcirculation, arrhythmia, encephalopathy, IEM, PRES, etc. Additionally there are many cases admitted to the PICU with diagnoses dealing with the surgical specialities including pedi surg, neurosurgical, ENT, plastics, urology and ortho. Besides the pedi surg cases, these patients are typically less interesting than the strictly medical cases, IMO, e.g. a post-op scoliosis or craniocynostosis repair in which there's not all that much to do besides pain and airway management and monitor for complications.
If autonomy, responsibility and respect is something very important to you, there's really no speciality within pediatrics with more of this.