You can either enable or disable the recent programs list from Taskbar and Startmenu Propteries, but when you disable those, the list gets cleared automatically. Again if you enable them, the programs originally present will not be restored (the default programs in your case). This is because, after enabling recent programs, no programs have been opened by you.
One thing I can suggest is, for the default programs like Calculator, you right click on each program and click on Pin to start menu. This will make the program present in the start menu, with recent programs being disabled. Again, those default programs will not be restored. You can find a list of default programs in the following image, which you can manually search and pint to start menu:
