Take heart and don't beat yourselves up over it.
It is a hard time... but there will be many moments of childhood that are not easy and we as the Mommy and Daddy... has to coach/comfort/provide understanding/safety/and loving for our kids.
*My son, was a binky user. But ALL day. Not just at bedtime. We gave the binkies to "Santa" too. But he also has a stuffed cow, which he sleeps with and it is his well loved buddy, and he's had it since he was a baby. So I think, that for my son at least, he adjusted well. It took him about 2-3 days.
You are all in it TOGETHER, this phase of his life. Obviously it is not easy for him. He is frustrated and "misses" his binky. All kids react differently. Don't think about should've/could've. This is what you did, and you prepped him too. And he understands mentally, for what he is able to at his age. "Emotionally" that is a different story. Young children, or even teens for that matter, can intellectually understand something, but not that their "emotions" are in line with that or keeping up with their literal understanding of something. ***ADDING THIS: have you ever broken up with a dear boyfriend Or been dumped... knowing mentally that it was for the best....BUT still being "sad" over it or upset or even "resentful"??? Well for a little Kid, this could possibly feel like it sucks too or he may resent it that it happened. Even though they "know" its for the best as Mommy & Daddy explained. The Binky was his pal. My son, would call it his "friend." No matter how well someone understands something mentally, it can still suck. It takes time.
Encourage him to communicate about it... to channel his frustration and "missing" his binky in other ways... let him punch a pillow or something.... redirect his pent-up angst about it. Let him know he is doing "good" about it... but you "understand" about how he feels... validating him. NOT battling him about it or making him feel worse about it.
He is probably in his own way... trying to be "brave" about it all... but alas, a 3 year old can only do what they are capable or mature enough for. Thus "Us"- WE can help weather the storm about it, keep things in perspective about it (being glad he did give up the pacifier etc.) and then be patient. But of course... convey to him that to be mean/hurtful is NOT allowed. That you are ALL FAMILY AND A TEAM about it, and WITH him.
To a kid, they may even feel "singled out" about it all because afterall, he DID stop his pacifier... but yet he is still getting chided about it/scolded/punished/given time-outs and what not.
I imagine this is a real hard time for him.... let him get it out of his system... but explain, that being hurtful is NOT allowed. He can express his feelings.... the best he can... but physically lashing out it NOT acceptable. AND ask him is he needs any "help" in his transition... anything that can possibly help him feel better.
Kids this age, cannot always "do" what they have in their heads. Thus, he is probably at a real conflict over it all too... which he is venting about, although he does not know "how" to vent, appropriately. The Binky, was also probably a way for him to "cope" with anything that bothered him. Now, he does not have anything to "help" him cope. He has to learn new ways. AND also though, 3 years old is a hard age developmentally... harder than the "Terrible Two's." A great book is: "Your 3 Year Old" which you can get from www.amazon.com
He has a LOT of things on his plate right now... at 3 most people expect a kid to be a "big boy" but they are still not yet a "big boy" and is a sort of hard age. Lots of expectations upon them which they cannot yet fully handle or understand yet.
All the best,
Susan