Thought I'd address some of the X-ray issues.
Ultrasound The ultrasound sound beam is attenuated by tissue- the more fat the beam has to penetrate through the lower the beam intensity. The lower beam intensity the poorer quality image. You can try and ameliorate things by using a lower frequency transducer, positioning the patient, using special transducers (e.g. transvaginal or trans rectal transducers) but there is only so much you can do.
X-ray: X ray photons are scattered ( degrade image / don't give useful information) by tissue. A large amount of fat means more photons are scattered. You can raise the X-ray tube and current to better penetrate tissue but then you lose image contrast. You can increase exposure time to improve image quality but this leads to motion artifact and increased radiation dose. In very obese patients much of the radiation dose is absorbed by the excess fat. You can try and improve imaging with tight collimation of the image or positioning the patient to present the minimum fat in the field of view and use things like a grid (helps avoid detection of scattered photons) /use special bariatric machines etc but really there is only so much you can do.
CT/MRI - A huge problem is the weight limit of the table and the diameter of the aperture for the patient (a patient's weight and/or girth may limit their ability to fit in the scanner) Bariatric CT/MRI/open MRI can help but are not a perfect solution by any means and the very large might not even fit those. CT has similar problem to X-rays - fat attenuates the X-ray beam. With MRI a large body habitus means a more 'noisy' image i.e. poorer image quality.
Nuclear Medicine/Pet scans: A large body habitus increases photon scatter/attenuation and the result is poorer image quality. Additionally it may not be possible to give the optimal dose of the isotope needed to image (dose is calculated by kg and there is an upper limit so the very obese will not be imaged optimally because the dose they need exceeds the safe upper limit).
Mammography: Large breasts (or even small breasts on an overall obese woman) make positioning more difficult (poor position = increased risk a lesion will be missed/obscured) and multiple images might be needed to cover all the breast tissue (so increase radiation dose). Additionally - large breasts can make lesion localization harder (the consequences of doing a biopsy in the wrong area are obvious).
TL:DR Far from ignoring the issue of the obese patient - there has been a lot of work in devising better equipment, imaging protocols, imaging algorithms etc to try and improve imaging in the obese population. However, there is only so much you can do because science truly is a shitlord. The sad fact remains: obesity degrades all medical imaging modalities.