First off, I really hope the OP was just posting an exaggeration, the original shot is far from a "perfect portrait"
- the top of her head is cut off (though thats a photographer problem not a camera problem)
- even at this small size I can see pixelization and JPG artifacts
- the direct on camera flash (I'm assuming) is not the most flattering and FAR from perfect lighting for the perfect portrait
- the fake bokeh and halo effect is far from convincing
I could go on, but I won't. No, I don't think you need a $7000 lens to take an amazing portrait, and yes, I think there is a diminishing returns as you spend more and more on camera gear. I also don't think that anyone with a $7000 lens automatically takes better pictures than someone with a $30 thrift store Pentax K1000. Artistically, the only thing more expensive cameras give you over say a Holga (the seeming gold standard of low-tech, low-cost gear) is control over what you have in your mind versus what you can actually capture on film/sensor.
Technically though, yes, more expensive gear does play a role in photography depending on your goals/requirements. How big do you need to blow the shot up in a print? What are the minimum file sizes required by your intended outlet (stock photography, magazine, client).
In the end, your gear dictates and your PP ability dictates the limits of what you can capture and present, your artistic ability is what allows you to reach that potential. Example: There are some amazing photos taken with Hipstamatic/Instagram and an iPhone, but the limits of the technology means they're only really good for small prints or web viewing. You'd never be able to submit those shots for stock photography or a juried show due to the file size limitations and JPG artifacts. I think you can take an AMAZING portrait (I don't believe there's such thing as a perfect one) with an iPhone, but there's limits as to what the lens and sensor can capture, you wouldn't be able to realize every shot you can create in your mind with that equipment.