jpeg is a file type, basically about compression. While it is limited in some respects in color, problems in color you describe are about proper conversion to sRGB, and no matter what you do the result will rarely look like your managed workflow. As photographers we set up our displays to simulate what we will get when printing. As such the display cannot show what the average viewer will see.
but then what display would? the entire thing is completely hit and miss ... since the monitors of the those viewing the images vary wildly, and you don't even know if the OS/browser is color managed.
I have a few personal opinions,( which most don't share), I think that almost every display out there is much brighter than mine, and is also cooler than mine. So I have a second display calibrated for sRGB, 160 cd/m2 and 6500k WP. I try to make sure my web images are slightly darker and slightly warmer, and they look pretty good on both my calibrated display and my web display.