Designing website for high-resolution displays is (at least for now) a trade-off between page-load speed and user experience. Page load speed definitely affects page rank. User experience can effect bounce rate, but it’s a gray area. So there are a few options to consider…
Does the detail in the image warrant the use of supporting high resolution displays? If the image is of a product, let’s say a very high-end, expensive bicycle, and it has text on it that describes particular features on the bicycle that someone would really want to see up close, then I would say a high res image would be justified. Using a standard resolution on a hi res display would result in blurry text, and unclear features on the bicycle.
But if the image is something where fine details are not especially crucial, but the speed of the website is, it might be a better choice to forgo using an extremely high resolution image to save a 1/2 to 1 second on the page load.
The below image is essentially the difference you’d see looking at your website on the vast majority of mobile devices, tablets and laptops in use today, vs looking at it on a 27" retina display.
From 5 feet away, your could barely tell the difference. Up close you would see it. Now consider that for mobile users, you’re loading a 1794 x 1500 pixel image on a screen that is probably 360 x 640 pixels. A phone at that resolution with a retina display would only require your image to be 1440 x 1204. Exported as a jpg at high quality (60) from Photoshop, that’s a file size difference of 236k vs 155k, almost a 35% reduction.
But if your client really MUST have the highest resolution image, then you can always use media queries to query the display being served, and select the appropriate image.