Not all of these files to be downloaded before you start using the page. 'Below the fold' content (which initially sits off the bottom of your screen) can be downloaded while you're reading the content at the top.
For some sites, below the fold content is massive. The 'height' of the Daily Mail homepage is 5.16 meters, with less than 10% of the content initially visible. In one sense this approach is quite wasteful of internet traffic- the Daily Mail will send you all 5.16 meters, even if you never scroll past the top 30cm (assuming you don't click away elsewhere). But internet traffic is cheap, so the Mail isn't unduly worried.
The net result of larger and richer pages has been steady growth in 'page weights' - the amount of data that makes up a web page. They are now averaging a little over 2MB on the desktop:
Source: HTTP Archive
Technical change in Oct 2012 means data on either side not comparable
It's a toss-up whether this growth is exponential (20-25%) or linear (+345 KB/year), but either way it's substantial and ongoing. That means more traffic for networks to carry, and more bandwidth needed to ensure web pages load briskly. (In practice, for technical reasons, latency is often a more important factor than bandwidth, and beyond 5 Mbps there seem to be diminishing returns).
However, the growth in desktop website page weights is not the whole story - the mother hippo has been joined by a baby hippo. In recent years there has been a massive shift to mobile consumption, and page views from mobile devices now represent almost 40% of the total. (In Africa it's over 60%).
This matters in the context of page weights because mobile pages tend to be much lighter - roughly half the weight of fixed pages. For mobile devices web page designers need to be conscious of higher consumer data charges, they need to fit their content into smaller screens and so on. Consequently both the number and size of files transferred are lower.
Weight average based on UK traffic mix
Clearly mobile page weights are growing steadily too, but because they start so much lower than desktop page weights, the shift to mobile is suppressing the growth in average consumed page weight, just as that hippo calf has reduced the average hippo weight in the enclosure. While desktop pages have been growing at +345KB, the average consumed page is only growing at +230KB.
However, baby hippos don't stay baby hippos, and once the transition to mobile devices is complete, the growth in average page weight will accelerate again - unless of course we've shifted all our usage to apps by then, which are even lighter than mobile pages.