Are there rich fossil beds underground everywhere, just inaccessible do to their depth?
It is my understanding that fossils are available over time due to erosion or the drying up of water sources which heretofore covered the mud under which the fossils lay. A prime example is in Egypt where not exactly fossils but historical monuments are constantly uncovered by the winds over time. Same with fossils as water and other erosive elements cut down to a certain time in history making available those dead critters which lived then and whose bones have become calcified and filled with the surrounding elements creating those fossils.
No. There are large areas where all the sedimentary rocks have been scrapped off by glaciers, for example in Canada, in NW US. The same is true for many mountainous areas where the sedimentary rocks have been eroded off and the old igneous and metamorthic rocks are all that is left. Most sedimentary rock layers do not have abundant fossils in them. However, there are some, especially limestones, that can have a lot of fossils, and in some cases they can cover large areas. I think that rich fossil beds are not common in most places, and they would not be found underground in most places, although that is hard to guess accurately.
The vast majority of fossil beds do indeed sit underground in Limestone and Dolomite beds within sedimentary basins. What you see at surface is only a very small preserved sample of what covers the Earth through Geologic time. I see thousands of fossils that most people will never see in the cored sections of wells that targeted oil deposits. There are hundreds of thousands of feet of preserved cores just in my Province's Core Laboratory Warehouse. Geologists reconstruct paleoenvironment, in part, based on these cores!