For example, while writing an erotic scene, is it important for the author to feel the same way as they expect the readers to feel when describing the scene?
For some subjective feelings or emotions, I'd say its a good gauge for the first draft.
If you think you are writing an erotic scene and your first draft of it doesn't seem erotic to you at all, then you are probably on the wrong track for an erotic scene.
The same goes for a romantic scene; if you don't find it romantic (on first draft) then your readers likely won't either.
(I will go into erotica and romance more below.)
The same goes for humor. If you write a joke even you don't find humorous on the first draft, it is unlikely to make others laugh.
The same goes for "reveal" scenes of awe or surprise. Capturing these kinds of emotions is tricky, if your first draft doesn't capture it even for you, then you probably haven't captured it for readers, either.
I emphasize first draft because some scenes lose their power, slowly or quickly, when re-read and edited and re-read again, for 3 edits or 30 edits or however many you do. For this reason you also need to be wary of an endless rewrite trap, where something seems exciting at first, but after seven edits no longer seems exciting so you rewrite it, and after seven edits that no longer seems exciting so you rewrite it, ad infinitum. This doesn't mean you cannot edit something, or cut it or find better words or sentence structure. But for scenes like these, do be aware of the phenomenon and try to stick to the original blueprint of the scene that made you feel something.
On romantic/erotic scenes in particular: Your story may call for such scenes that are not in your own wheelhouse, that you don't find particularly romantic/erotic. This may be true for scenes between characters not of your own orientation, or using tools (bondage, pain, costumes) or playing roles (rape, slave) that turn you off.
One approach to this dilemma is translation. The idea is to write a similar romantic/erotic scene you do find erotic, between characters with similar personalities to your characters but matching your own orientation and proclivities. Whatever actually does feel romantic to you, or erotic to you, so you can bring those feelings to the prose. Then follow that same blueprint for your actual characters.
Translation operates on the assumption that ultimately the feelings of romance, love, lust, sexual excitement and orgasm may vary in intensity but are pretty much the same for everyone. It is just the "ways and means" that change from person to person, by which I include the traits of the person that attracts them, and also include any props, setting or language they find necessary to achieve their preferred altered state.