Strange isn't it? They've done so much to improve it in other ways.
Most textbooks that we buy these days have CDs with a PDF version of the text so I am generally working from Acrobat rather than from on-line material. I use "print to ON" to capture whole pages but if I want just one portion of a page then I use the snapshot facility in Acrobat to capture just a that bit to the clipboard and then paste to ON.
If I'm working with on-line material then there are two approaches I use. One way is to use SHIFT-PrntScrn to capture to the clipboard, paste into Word, clip there, then paste into ON. This is longwinded and you lose image quality (such as it is from a PrntScrn). A better way is to use a screen clipping facility to capture just a portion of the screen (such as Corel Paint Shop Pro or one of the many freebies). Of course you have to accept the resolution of your screen. Firefox will at least allow you to enlarge your screen and thus get a better result but then you have the problem in ON that the only way to resize is by dragging a corner. You can't resize an image to a consistent size as there's no equivalent to Word's ability to size to a percentage. You can also just paste the images and text in separately via right click & copy on each separate element of the page. Tedious but works and gets the best possible resolution for images.
I really can't understand why they didn't incorporate both of these abilities (resize to % & clip) into the new ON! It's not as if either of them are going to be hard to implement and they are both obvious needs. Hopefully someone who's good with C++ will come along and produce an addon. (Pretty pleeeez....)
BTW - have you discovered in your exploring the option in ON that lets you specify where the result of a "print to ON" goes? The default is to have it put into the unfiled notes section (I think) but you can instead have it ask you and (for example) have it place the image onto the page you've just been working on.