As the title says, I see most web hosting companies provide plans that running Apache instead of Nginx. So, what is the reason that makes them stick with Apache? Although, Nginx is much more lighter and not heavy resources eater as Apache!
Simple answer. Hosts provide what is asked for and works best. It is a double-sided coin. Apache has been extremely successful and is stable and seasoned code therefore hosts don't have to work hard to support it. As you may know, Apache is one of the first successful web servers and serves the vast majority of web installations therefore it is asked for the most.
I used to be a webhost in a prior incarnation. While you may want to experiment and try new code, in production installations where revenue is on the line, discipline and standard and stabilized builds are the only way to success. For example, if you start installing code that has a vulnerability and the system becomes compromised, then you can potentially take down an entire business. I had a system that constantly checked the customer web spaces for installations and checked that they were stable versions. If there was a compromised or unrecognized software install, it is automatically disabled and manually checked by a tech before allowing to run if at all.
Hosts that are permissive do not last and those who are disciplined succeed. This is not to say that Nginx is not good software and would not be welcomed. It may be that there is not customer enough demand to seek out a stable build for Nginx. Keep in mind that it is not just Nginx that must be looked at when considering a build. There are many moving parts and therefore the complexity is something to consider. Having said that, I suspect you will see Nginx more in due time. Forward looking hosts that are careful with their builds can certainly offer Nginx as long as it is stable and plays well with others.