My experience is that it's often content on the page or coding that doesn't quite work on mobile safari. Also, given those types of sites, it may also be flash based content - which mobile safari doesn't play (and Flash is a dying program anyway)
I would suggest that you see if that news source has a mobile app or look for a different browser.
The site is highly unlikely to change their coding to accommodate mobile (although in this day and age they should) nor is Apple likely to tweak Safari for a site or selection of sites (the expectations is that companies/people fit in with their business model not the other way around), so the only real thing for users to do is to find work arounds, which would be an app or different browser.
I use Atomic web browser (no idea if it has a cost or if it was free, it's been a while since I installed it). I've found, given mobile Safari's eccentricities it's always good to have a different browser available.