That was a HUGE wall of text! Would had been better as a video because many people won't want to read all of that... Anywho I read over all the main points regardless.
I'm gonna be as understanding and respectful as I can here while also being honest. First off and I don't know any other way to say it, my opinion is you have a warped view on a silly cartoony hammer and how you also relate it to Amy's character. Yes I'd agree I don't like how her personality is portrayed lately... but my opinion is all Sonic characters are mistreated and handled poorly nowadays. To me the modern portrayal of even modern day Sonic himself is awful and he is nothing like the Sonic I think of him as anymore. However I don't agree Amy needs to be a nice loving sweet heart girl to such extremes that you do in order to fix her character.
I don't agree that her hammer can't be integrated better into speed based gameplay. I LOVE the Hammer drop move. Sonic Advance's gameplay for her can easily be improved on... And they even started to do that on the next games where they added rolling for her, and yes I'll agree that she should be able to roll because absurdly even Tails can do it... I'll say that even despite the fact that I prefer characters to have more unique gameplay over being mere boring clones with small added powers on top... which is something me and many Sonic fans won't see eye to eye on ever. I don't disagree with characters using the same base... but I feel far more should be done to them to make them differently fun then just 1 or 2 added on small powers. Simply making Amy a pink Sonic with a added high jump or something basic like that doesn't do it for me, not in the slightest... It basically would just be better then nothing, which in my book is not good enough.
Next I'll comment on is the more or less whole "Think of the children!" parts which does not amuse me one bit as I hate those kinda arguments, which are often used as a cheap excuse to just manipulate people. Her hammer by itself doesn't make her a bad character or a bad influence on kids, and I won't entertain that thought process. Even heroes with a heart of gold can wield a battle hammer. You say you loved the concept of pre-hammer classic Amy with the idea of her being a sweet girl with a nearly pure heart aiming to be a hero?... Yet are we just going to ignore the obvious here and how her nickname was Amy The "Rascal?!" and the fact many Sonic characters are designed and known for their bratty personalities? I know I sure didn't forget, and it's part of why i like them. Sure Amy isn't handled good in her modern incarnations, but she should never be made into something she isn't either. Amy needs some spice to her character, so them playing up the whole "rascal" angle would be ideal if done correctly.
Lastly I'll say this. The real question is why do you think we all need to know why you dislike her hammer to such a degree? You act like you are not trying to change the opinions of others... which by the way I do not believe whatsoever. People almost never say things over and over and over on open public places just to hear themselves talk/knowledge their own feelings to themselves. Lets be real here, you feel alone of your thoughts on this and want to see at least SOME people agree with you, and that is understandable. But I say that is it REALLY necessary to beat it into our faces your opinion on a single subject at almost any chance you get? Some advice. Feels like half the posts from you I've seen discusses the same subject with you never letting a chance go by how much you hate her hammer. Am I saying for you to stop? No. But maybe lower it down a notch? For example you know how annoying it would make me seem if I kept on ranting on about every chance I got how I think Blaze is the among the top best Sonic characters and deserves her own spinoff game series? It would make me unbearable... hell i would be sick of me if I did that... And yes I have gotten sick of my own behavior before, I just took a step back and looked at everything with fresh eyes and realized how overbearing I was being. Anyways I'm not saying this to be rude to you or to get you to stop, just advice how I think you could handle it better.
On a personal note. My first encounter with Amy in life was on Sonic The Fighters which was inside a chuck e cheese during the 90s. I have good memories of that game. To me it's not Amy without her hammer. When I see Amy in Sonic CD... all I see is a early prototype concept for her character where Amy was not interesting or meaningful until later on in the series... And just to say, MetalSonic also was not used good enough in that game itself despite all the heavy advertisement for him. Really was a game with tons of miss opportunities and unflushed out ideas.