You are correct. It is a good general practice to align the printer when new cartridges are installed, but it is not a requirement. The alignment is done for print quality purposes. On this printer, the printhead is built in to the ink cartridge. When a new cartridge is seated, it may or may not be in alignment. It sounds like your cartridges are in alignment.
You might try shutting down your computer (not a reboot) and doing a Hard Reset on the printer as described in the following link. Click Here After you restart the computer, is there a difference?
If not, and the print quality is good, I would recommend skipping the alignment. If you want to be able to do an alignment, you might try doing a complete uninstall of the printer software and downloading and installing drivers from hp.com. Click Here