Why can't we use a combination of cables and satellite for internet connections?

This does happen already. I worked with a system ~12 years ago which used satellite outbound from London to the Middle East and then local connectivity over telephony networks for the return. Typically internet traffic is asymmetrical, most people, most of the time download more than they upload. So having a faster download via satellite and very basic upload via low quality phone lines is practical for consumers. It doesn't work for those who need to upload and VoIP tools like Skype don't really work with it. The good news is that even a mobile phone link can be boosted to over 100Mbit/sec via satellite (in practice the limited uplink might restrict requests and ACKs making lots of downloads on a small uplink difficult). Traditional bidirectional satellite links require calibration and expensive hardware. One of the biggest advantages of this type of asymmetrical link is that it can be used on very low cost equipment and installed by non-specialists. If anyone wants to deploy such a system (on a commercial scale) then let me know, I might be able to help.