We all have habit words (one of mine is "bit." Whenever I search for it, I dope slap myself with an accompanying "doh!" I'm not interested in eliminating it, but I don't want it to look like I've been paid by the society for the use of "bit" either!). If "suddenly" is a habit word, then yeah, worry a little. It should not be a lazy default, but as some have pointed out, there is no reason to eschew the word entirely. It's in the language for a reason. In truth, I think it is overused, and a writer should take a precaution or two to see if they have done so. My objection to it is essentially that it is what I call a one word oxymoron (I collect those). Suddenly just ain't. It's a three syllable oxymoron with a comma or implied pause after it often. That's one word, meaning pretty much "instantaneously" (another one word oxymoron), that takes four beats when you are reading. "Suddenly" just isn't a sudden word.
However, I have used it 49 times in 250K, and that's after vetting for it. Where it works for me is when it is used as a transition. An abrupt change sometimes needs a transition, a notification to the reader, "listen up! Pay attention here!" I fervently agree with using the right verbs; verbs are the engine of a sentence. A good one takes you far, a bad one has the whole thing breaking down. But sometimes that is not enough. Sometimes a sudden action needs immediate notification. There are places where I use good verbs, but when I read the sentence without the transitional "suddenly," I slide over the change in action, and go, oh wait, using an entire sentence to be sudden didn't give the feeling I wanted. It diluted the full stop that suddenly provides. So while suddenly isn't sudden, sometimes to best be sudden, you have to stop the action that was happening right HERE...suddenly. That can sometimes be the best way to knock a reader...suddenly. So even though its a four-beat stop, or maybe because it is (meaning it provides a firm and noticeable point of transition), "suddenly" sometimes is the best answer.
Because of all this, "suddenly" should be a conscious, well considered choice, never a habit or a default, for if it is overused, it will lose it's power where it is correctly used as well as where it is not.