I've tried this on Monterey 12.3.1 with the BBC website and am not seeing any issue. Is it a specific website which is having this issue or are you experiencing it on many? What version of OS are you running?
Now that is interesting, I too can see the problem. It's interesting the images on the pages are actually are embedded images from Pinterest. Perhaps they block or not load the same when the page is generated into PDF.
You could try (I haven't tested it) saving the page as a Web Archive. Safari (File>Save As) offers the choice in the Format pop-up at the bottom of the Save As dialogue. This promises to save images, amongst other things.
If you specifically need a PDF, you should then be able to open the archive and export a PDF from it.
Although saving as a web archive works (and looks as though it is embedding all of the images), exporting a PDF from the web archive does not -- the images are missing again.
It appears to be related to the loading="lazy" attribute on the offending img elements. If I try printing this article as a PDF, for example, the first image (which does not have the attribute) is included, but the subsequent images (which do have it) are not.
One solution, although a bit tedious and fiddly, is to open the web inspector on the original page from Safari's 'Develop' menu, and delete the loading="lazy" attribute from each of the img elements that have it. Then exporting the page as a PDF does include those images (this works both in Reader mode, and without it).