Numbers app lists all file names
When we go to a program we go there to create a new file or
  resume work in one.


Or, we may want to open a file that was created with another app. For example, we may have created a CSV (Comma-Separated Values) file with another app and want to open it in Numbers to format it as a spreadsheet.


  When one clicks the Numbers Application icon Why does
  Numbers in Mavericks list files with different extensions
  and not just Numbers files? 


Numbers shows you all of your files, because hiding some files is disorienting and prevents you from finding your way around the file system.

However, notice that some files are grayed-out within the Numbers Open dialog box. Those are the files you cannot open with Numbers. If a file is not grayed-out, then you can open it (or Quick Look it) with Numbers. This includes many files that are not Numbers documents, or were not created by Numbers, such as Excel spreadsheets, or text files of all kinds.


  Only Numbers files are allowed a "quick look" and nothing else.


That is incorrect. If a file is not grayed-out because Numbers can’t open it, and you can Quick Look it in Finder, then you can Quick Look it in the Numbers Open dialog box. Try Quick Looking an Excel spreadsheet or any kind of text file.


  This whole thing seems like a waste of time.


If that is so, then toggle the Numbers Open dialog box from “On my Mac” to “iCloud,” where you can Save your Numbers documents in one flat hierarchy of Numbers-Saved documents. That way, when you activate Numbers, you can choose only from the documents you previously Saved with Numbers.

Numbers is giving you a choice of 2 ways to work: iCloud’s straightforward “Numbers owns these Numbers documents and that’s all I want to see,” and the “On my Mac” method of incorporating files into Numbers that were not created by Numbers, and which may be Saved in arbitrary places in a larger filesystem. Some people prefer one way, some people prefer the other. It sounds like the iCloud method is right for you.