Yeah, I teach my students to use broom on the models and then make the plots with the resulting data.frame. But I've been trying to find some shortcuts because it gets old copying and modifying the 20 or so lines of code needed to replicate what plot.lm() does with 6 characters.
Yes, DRY, so I should make a function, and I have, but it's not working very well.
"From what I can see ..." -- where? is this done inside ggplot()? I looked for a ggplot.lm() method but ...
UseMethod("ggplot") is telling you that ggplot() is a (S3) generic function that has methods for different object classes. So we can list all the methods of ggplot() with the methods() function.
 ggplot.data.frame* ggplot.default*
see '?methods' for accessing help and source code
which tells us that there are currently two methods for the ggplot function. UseMethod will use the class of the input to figure out which method to use.
In our case was the output of an lm call which only have 1 class, namely "lm":
class(lm(Sepal.Length ~ Sepal.Width, data = iris))
ggplot.lm does not exist in the available methods as you correctly have noticed which leads UseMethod to fallback to look for a default method. That is, it looks for ggplot.default. Which it finds and calls. And if we look at the source code for ggplot.default we get the following