The risks are higher because you are introducing more fail points into the system. As much as I dislike the swiss cheese model, I'm going to use it to illustrate the difference between a constant descent and a dive and drive approach.
Potential fail points both share:
-Setting the wrong MDA - So, like, it's somehow easier to set the wrong MDA than the wrong DH? They're both in black and white on the plate.
-Not finding the airport and having to go missed - How is this more likely on an non-precision than a precision approach?
-Course alignment errors - Wait, so they're more dangerous because you might forget to read the plate and make the number in the little window match the number on the piece of paper? Maybe you'd "find your bliss" better as a Sanitation Engineer?
Potential fail points a constant descent has:
-Not getting down in time to see the runway and having to go missed - GO MISSED? My God, that's basically an accident right there! Also, expecting a pilot to get the aircraft to an appropriate altitude before commencing an instrument approach is "difficult"? Consult aforementioned PTS. Amazing anyone ever gets a rating!
Potential fail points of a dive and drive:
-Multiple stepdown fixes that could be set wrong - Yeah, it's pretty tough to look at the DME or God Forbid set a cross radial. If you could do that right every time, you'd be in third grade! I'm not in third grade, are you!? Dangerous.
-Multiple large power changes (which is the most likely time for an engine issue to occur) - Looking forward to your litany of accidents which have occurred because some poor bastard was forced to move the power levers during an approach!
-Potential for leaving VDP/PDP early and hitting something - Again, reading is pretty hard.
-Being unspooled for large portions of the approach during a potential shear situation - This should be another long list of accident abstracts. I'll just get me reading glasses.
-Much higher fuel burn (and noise issues in sensitive areas) - Well that does seem dangerous.
Your argument about the fact that 707 pilots could do it is a straw man, and a poor one at that.
Howso? It seems to me to be a direct refutation of the claims that it would be somehow absurdly dangerous to shoot a step-down approach in a large aircraft with slow-spooling jet engines? Cause, I mean, your high-bypass turbofans are Le Mans next to the ole straight pipes, by all accounts.