As someone who was on the receiving end of a very good friend's style intervention, I have a different take on things. [We had 20 years of history, but it sounds like you and your friend are very close.]
For me, the "intervention" really was the proverbial wake up call and one that both made me come to terms with a lot of body image baggage and a lot of other baggage about not wanting to be seen as "showing off" by dressing well or to stand out. FYI, I dressed a lot like your friend...black n' baggy was my uniform 99% of the time.
My friend approached it the way you are contemplating -- "it kills me to see you hiding your cute blah blah" and "look, we are [at the time]in our mid-30s and you should be celebrating who are and reflecting your personality with your clothing before you're dead."
Of course I became a bit defensive, and had a million reasons why I was the way I was [lacking money for clothing being a big reason, though there were ways around that had I been interested.]
But I respected her as a person, and she always look GREAT and "pulled together" and she had a lot of career success that I wanted for myself. So...her comments made me start thinking, and reading about body shape, and going through my closet...SLOWLY.
It probably took 6 months til I started buying a few things that FIT. And another local friend had to convince me they weren't too tight. Five years on I tell Intervention Friend she created a monster!
BTW, I also paid the controversial "favor" forward this summer...to a friend I've known almost 30 years! I think she was a tougher nut to crack because unlike me she didn't have an innate interest in color/textiles/style/fashion.
She fought hard so I didn't push things too much. Now she has started to buy a few lovely things in styles that *fit* and colors that made her look gorgeous...and she got lots of positive feedback. [And she still speaks to me, ha!]
So obviously I think an intervention CAN be done if it comes from a place of caring and the people on the receiving end aren't so fragile that they will spiral into major depression/break off all contact with you.