Okay, big thanks to @RyanReese (who found the spec for me and solidified that I was on the right track), but unfortunately this is part of the CSS2 spec.
Visual formatting model details (search for 150)
In short, Chrome or whatever browser you are using is enforcing the 150px iframe size (so long as they follow the CSS2 spec).
So how do you reduce it or enlarge it based on the content of the iframe? With JavaScript 
There isn’t a CSS solution that can tell you the height of the iframe content (as that data exists on another page/site). So unless you can execute some JavaScript to get the inner height of the iframe before it is cooked, Discourse just has to pick a happy medium to ship with.
If you can, the idea would be to detect if it is greater than 100px, if it is, set the height style and max-height to 300px (to give it some room to show the user what data is there. Otherwise, set it to 100px for both attributes.