The F104 didn’t have any lift. One engine hiccup at low altitude and it’s a dirt nap.
“Thud Ridge” got that name for a reason.
Those stubby little wings were still airfoils but they did need speed to generate lift. That's where a big engine came into play - but it was only one engine & a significant burp at low level would mean a critical test of the ejection seat & pilot ability to fire it off in a very big hurry.
Not the only military jet with brick-like glide path but probably the prime example..."anvil" wasn't an uncommon nickname for the F-4.