This is in reaction to a post on Google Plus complaining about why the BBC mobile site wouldn't serve large images to a phone that is capable of downloading and displaying them. (This is current practice on many mobile sites, as it were.)
So, the BBC website is also serving developing countries, where the best mobile infrastructure consists of what in advanced economies is essentially legacy technology. For example, only this year did Pakistan begin adopting 3G.
Many sites are not necessarily willing to incur additional bandwidth costs, unless they were ready, willing, and capable of serving very large amounts of content (such as YouTube).
Another typical issue is with designers of lesser websites, who fail to optimize their content.
Mobile data connections incur charges for data, which can be substantial for people with limited budgets. Thus a major factor to consider when designing a mobile site with worldwide viewership is responsible data usage, which then requires designs that are made for the lowest common denominator.
Because when people must pay money to read a website, they will avoid those that are expensive to visit.
AFAIK, there seems to be no easy way for a site to automatically detect if a user is visiting through 2.75G (GRPS/EDGE), 3G or 4G. The best indicator is the user agent string, but that doesn't always tell if the phone is actually on the net via 3G/4G; only that the device is capable of such.
If phones were able to report through the user agent string that they're browsing via 3G/4G, or even better — if a device were able to report its download speed on a certain network/infrastructure, websites would be able to fine-tune the content served to their various visitors. Unfortunately, this would be ripe for abuse, if content providers began actively excluding devices with speeds and connections under a certain threshold.
Another point to consider is that when mobile phone users are tied to a limited data plan, they are not willing to download more than absolutely necessary. This being text, and more would be large images.
A solution could be for mobile users to select which connections they would want which version of site. If people have a limited plan, they'd want small content; if using a dedicated connection over Wi-Fi, they'd be content with bigger images.
There are some solutions (or workarounds), such as one based on cooperation between site and user by implementing cookies to select the lite or heavy site, if such functionality is offered. There are also apps for mobile devices.
Another possibility is for users themselves to specify which version of a site they want to visit at a time, especially if a mobile version is on offer.