Can I put Hardie Backer right over the drywall and then tile?

It depends..
Is the tub or shower base in place and will the thickness of the wall now be too far out over the edge? If so I would remove the drywall. (Note that 1/4" backboard is not sufficient to keep tile from cracking if someone leans on it. Note that Hardie board has wood fiber in it and needs 1/8" expansion gaps.)
If you can keep the drywall, put up a vapor barrier to keep mold out of water gets through the grout over time, and to keep any steel fasteners from rusting and popping.

You COULD do it but it might look like hell because of the additional thickness of the hardyboard on top of the thinset and tile. There aren't a lot of situations that come to mind where that thickness won't be important.

Is there a reason for not taking the time to remove that section of sheetrock?

In my opinion, the correct answer is NO, you should not install cement board over drywall.

Simply put, the existing drywall should be removed, the stud walls should be inspected (probably some nasty/moldy insulation behind the wall), and the cement board needs to be installed properly.

Mark