To me, using "asked" with a question mark is redundant. Using "replied" when the line obviously addresses the immediately prior statement is redundant.
Redundancy isn't always bad, but that's another topic. To put it simply, "asked" and "replied" are no more redundant than "said." But you have to use a word. The question, to me, is whether he asked it or whether he just said it. Not to make a big deal about it, but if you're looking for a right and a wrong, I think sometimes "said" can be wrong. We try to say that it's invisible, but if you really boil it down, "said" means that the words were spoken in a rather normal and straightforward manner. The question was not said out loud. The question was asked out loud.
But I'm only saying that because you're pressing. You're making it about a right and a wrong answer, and I'm responding in that way. But honestly it doesn't matter, and you should write in the manner that supports to your writing voice.
There's hundreds of ways to get across the tenderness of the romantic moment, the soft tone of voice, or any other perception. Adding an adverb to said only gives the writer two things. First, an economy of words. If for some reason you had to limit word count, then maybe I could see it. Still, I wouldn't do it myself. Second, it's an easier way to write, which is why I consider it lazy description.
This is assuming an awful lot about the context of a line to make a sweeping point. Even if this is all there is to it, there are plenty of times in even the most methodically well-written narrative that a short and easy line, I would say, can even be demanded by the context of the story, let alone appropriate. For instance, if the dialogue is happening quickly, a longer description can slow things down. Or if the emphasis of the moment is on other things, a longer description can be intrusive.
But why demand that authors need to waste words if "said softly" will do it?
Writers think modifying "said" gives the reader information they need, and therefore the use is justified. I disagree. If it's necessary information then it deserves proper description. What does "said softly" really give your reader? "Softly" could have many meanings. By itself it tells your reader nothing specific. It lacks clarity & steals emotion and power from the scene due to the unimaginative, nonspecific, and weak language. A writer is better off trying to depict the emotion of the scene through actions and dialogue.
I could replace "said softly" with "said," and nothing would change. Why give "said" the benefit of context to explain it, but suddenly if you add "softly," we're assuming it's vague with no context to support it?