I like Hetty, in the same way that I like Kitty, Lucy and Molly, but am not so enamoured of Kittie, Lucie or Mollie.
Yes! I have a first name that follows this pattern. One of my parents told me that with hindsight they wished they'd picked the atypical -ie spelling, because it was cuter and more girly. I told them I was very glad they didn't, because as an adult woman I don't want to be perceived as cute and girly. Having a name ending in an -ee sound without a longer version to fall back on is bad enough.