The difference in DOF is more of a minor technicality than a "Your 1500 dollar lens performs like a 350 dollar one!" though. OP is correct that you are exaggerating, though OP was definitely wrong to ignore the difference.
Here we go. The $350 on full-frame in all likelihood outperforms the $1500 lens that is heavily cropped by an APS-C body. According to DxOMark, the Canon 85mm f/1.8 has substantially higher overall sharpness than the middle 40% of a Canon 50mm f/1.2 lens.[1][2]
It is true that the cheaper lens has slightly greater pincushion distortion and vignetting, however both flaws are trivially (and automatically) corrected in post processing. What can't be fixed in post is overall sharpness and depth-of-field.
It all depends on what kind of photography you're doing, and your personal style.
For me, getting that shallow DOF is a nice-to-have, but it's not what I'm typically going for. More likely, I'm using a 7-14mm lens (on my m43 camera, if it you care), which for most reasonable compositions has infinite DOF if you just use hyperfocal distance.
I ignored it because when you get into practical image making the difference in image related to depth is negligible compared to the image quality to cost ratio. My point was that a small sensor can have a use, telephoto compression as a by-product of a crop is pretty handy when you have very expensive primes you want to make longer, hence i only used L series lenses in my example. I forgot there is tie between mastery, artistry and pedanticism. Source: The studio I co-founded won three Emmys for image production (Game of Honor, StillMotion was the production company) and had great margins.
In terms of equivalence, you're just mathematically wrong.
To demonstrate why you're also wrong with overall quality, consider the Canon 5Ds/5DsR. An incredible 50-something megapixels; famous for being able to reveal flaws in (or at least exceed the limits of) some of the most expensive glass. This is because its pixel pitch of 4.14µm is so incredibly fine.
The latest APS-C bodies, the 80D for example, have a pixel pitch of 3.7µm, which is even finer still. Using full frame glass on an APS-C body is like putting it on a hypothetical 5Ds Mark II and cropping into the middle 40% in post. It's just not going to be sharp.
This is because when you put that expensive full frame lens onto an APS-C body, you're only using half of the actual physical glass you paid for. The rest of it is going to waste. You're just using the middle bit... then magnifying it to accentuate the flaws.
And just so it's abundantly clear, I am not saying that APS-C is inferior because it absolutely isn't. Nothing is stopping lens manufacturers from making similarly good lenses for a smaller image circle.
The issue entirely boils down to using lenses optimised for one sensor size (in this case full frame) on a camera that has a significantly smaller sensor (in this case APS-C).
Also, I went through 4 or 5 85 1.4s to find a sharp one because the built quality was so bad, and even after a couple of weeks traveling it had gone soft, never found this with my 50 1.2 (although I ended up ditching all the crop gear and going to FF when I bought the 85 1.2) - However, it was a really good substitute till I could afford it (as I mentioned above) :)
