Why are there so many log files in a typical Linux system? Why don't they use one consolidated logs db/file and an api? I just wonder why are there so many log files in a typical Linux system? Wouldn't it be a better idea to have one system api function for logging and one consolidated table to save all the log entries from all the applications?

It's part of the Unix philosophy. The idea is that text files are free from program lock-in and everyone can use whatever technique they prefer. To take this further, flat files are often used, as opposed to markup languages like XML (although I have seen programs storing things in XML format as well).

In googling I have found this nice writeup about plain text, with comments about the Unix philosophy.