Let me speak to this because both my daughters looked into getting a MS in engineering (BME) after undergrad.
D1 was a physics & math double major with a chem minor. She was told by 3 different universities that she could not be considered for acceptance a graduate engineering program without first completing the equivalent to a bachelor’s in engineering.
D2 was a neuroscience and math double major (who took engineering physics and computer science classes). She took looked into getting MS in BME. (Because she specialized in instrumentation in her undergrad research and was working for a multidisciplinary academic team doing instrumentation development post graduation.) However, the university would only accept her conditionally with condition that she take 8-10 core engineering courses before starting her her master’s coursework.
A friend of D2’s double majored in math and cognitive science (neuroscience’s more computer-y younger brother), took engineering physics and applied for a PhD program in neural engineering. He was told he would only be accepted conditionally and the condition was he first had to complete 10 core undergrad engineering classes first. (While it’s theoretically possible to complete 10 classes in 2 semesters, due to course sequencing issues it actually takes longer, )
So @Ryan_Rd if your son decided he did want to do engineering, a physics degree would be helpful, but still would require him to complete the equivalent another full bachelor-level major and would take 2 additional years to finish.
Just one more datapoint for his decision.