Has it though? How often has an anime set forth to do something different to the original source material and I don't mean filler arcs because you've run out of material, or brand new endings, or weird pacing. I mean actually tell it's own story in it's own way. Plenty of shows created by less than talented staff turn out badly but I don't think that means anything for the very idea of making something different from the magna.
The original Fullmetal Alchemist isn't just a straight adaptation with a different final act, it's performs re-writes on the story throughout, inserts brand new material, expands upon existing material and completely re-arranges the way revelations are delivered to the audience. In the original manga, there's no explanation of the boys origin until Volume 5, that's after Nina, after Scar, after Hughes. The original anime series moves that right to the start of the show to create a core emotional and thematic base of the series and it's a great decision that completely changes how you view the series right from the beginning.
There are other examples too, think of K-On! which started out as a simple 4-koma gag strip. By the the time KyoAni have made the second season the show was completely different to the manga. Or think about how they decided to change the chronology of the storytelling when they made Haruhi.
When creators think about the unique position they're in when it comes to adapting a work into a completely different medium and understand the mediums strengths and weaknesses they can produce great, new works, not simple re-hashes of stories that already exist in a different form.
I'll agree, I don't think that the idea itself is bad, but it's just in general poorly done. Tokyo ghoul is a great example of this that is airing right now. Their changes in order of story and events have drastically changed characters and events for the worse. I was watching the anime having never read the manga before and having a lot of major issues with the main character and events... it turns out most of the main character being a completely gullible idiot is due to the way the anime was adapted and the change of details about how he comes to realize things and go do things. In the anime despite not being able to cut himself by ramming a knife into his gut... he for some reason random gets cut by a tea cup...
As for FMA being a completely different adaption... I both agree and disagree. indeed the start isn't a straight up adaption, but at the same time it is more just a well planned out series that went for the alternate ending route that you are trying to exclude from the very start (with the no alternate endings). It's well done, and well thought out but that is what it really is... just an adaption that didn't have enough source material that went for the alternate ending instead of a to be continued route... which the list can go on and on for series that have went the alternate ending route and had garbage routes because they didn't plan things out well.
As for k-on it might be different... but by no means do I consider it good.... I haven't read the manga but I actually liked k-on when it first started, as it went on I liked it less and less and eventually I grew to hate most things Moe thanks to it (plus the second season has a terrible squeaky opening :/) so perhaps I should check out the manga to that and see if there is less cake eating and falling over.
as for haruhi, I do agree that it was interesting with the chronological thing... but alas I can throw the same series right back in your face with what they did with endless eight... as that was also a unique adaption of that story and turned a lot of people off the franchise due to how poorly it was done.
I am not saying that unique stories compared to the manga are a bad thing, nor am I saying they can't be well done. But in general I just don't find them well done (for every good one I can think of quite a few that are worse), and that isn't because I am in love with the source material first. The vast majority of my manga reading over the years is watching an anime, hearing people complain about the changes they made, and then reading the manga and finding the original story vastly superior because a lot of changes made for anime just aren't thought out well. Again FMA was thought out well and that is likely why it turned out well... many others aren't though.
In general I prefer proper adaptions from the source material, and then after that exists if they want to revisit the series and give it an alternate adaption that is fine (such as the FMP route with fumoffu breaking up the first and second seasons (note: I am not sure if fumoffu has an actual source material or not... but it clearly is an alternate take on the series either way))
This does remind me though, I need to sit down and read code breaker as the anime was terrible and I have heard the manga is quite a bit different and actually decent :/