Q: Is iTunes 12.5.1 a requirement for syncing a device with iOS10.

There is no solution, nor has there been any solution to this issue since computers were first made.  From what I have read iTunes 12.5.1 was released to "support iOS 10", and iTunes 12.5.1 requires OS X version 10.9.5 or later.  Typically an iOS version requires the iTunes version that exists at the time of the iOS release, and iTunes 12.5 was released at the same time.

Apple nominally supports hardware pretty much as-is for 5 years. Hardware support in practice extends to 8 years as long as you do software upgrades. iTunes 12.5.1 would work on my late 2008 MacBook if I decided to install it (I am happy with iTunes 7.5).  Apple's response to you would be, "You should be running El Capitan on a 2011 Mac."  As for the older software the stock reply would be, "Upgrade your other software."  Once software or hardware enters unsupported status it is as if it had never existed, and your Mountain Lion has been replaced 3 times already and about to be relegated to 5th place when Sierra comes out next week.  Once a system is 4 years old and been superseded 4 times I bet they don't even try to run newer developments on it.

The real solution would be for Apple to stop breaking third party software and hardware every time it updates an OS. I'm really getting sick and tired of it, and it's why I stopped upgrading OS X on my Mac Pro, because I need to be able to open my old DAW projects from Pro Tools and others that require external hardware to run. Now, if I upgrade beyond 10.8.5, I must buy new hardware (or newer, used hardware, I guess) to support Pro Tools externally. However I have no idea which of my plugins will break due to Apple's increasingly restrictive system daemons like sandboxd that prevents from running correctly any Audio Unit, VST, and AAX plug-ins that are installed in the /Library path (which was common) because they changed the permissions rules for those folders to stop malware.

Well, y'know, I'm all for security, but they need to make manual overrides for these security settings when they break third party stuff. I am more than happy to never connect this computer to the internet. But I want to still be able to install my old versions of software. I don't understand why they must always break everything when they do these updates.

The answer is alway, "Well, just update your software." Well in the case of some software it's VERY expensive to update it. In the case of other software, it requires hardware that is also very expensive to update. And lastly some software gets discontinued and development ceases, and since Apple could give two f****s about backwards compatibility (since it makes them no money), then we are forced to keep our machines running old OS versions. The least they could do is give us some way to sync our phones, for crying out loud. There's just no excuse for this. It is really upsetting.

I mean, I get it, they will blame the third party developers for not having followed their best practices and ignored their deprecations, but the end user doesn't know or care about all that. The end user just gets screwed.

And honestly, there is literally NOTHING in the new OS versions that would enhance my Mac Pro for what I do with it. 10.8.5 is basically a perfect operating system. Yeah, Mission Control is kinda cool, and yeah, enhanced retina support is great, but if you're not on a retina machine, and you can live without Mission Control, everything else that's been added is just fluff that was merging OS X and iOS closer to each other in terms of interoperability. All of that could have been added in upgrades to 10.8.5 that did not require breaking of hardware and software.

All the breakage comes from their tightening down of "security" on the system, which I'm not convinced is anything more than simply an overzealous control freak type approach. It comes from the attitude people take to being a server sysadmin. If my machine was a server on the internet, and I'd hired Apple to be my sysadmin, then I'd let them do whatever security related stuff they wanted.

But this is my home computer that does not live on the internet all the time. I barely ever download stuff and I don't use Flash or Java. I just make music and back up my cameras and phones. So, locking my down system like it was a military server, preventing extensions that were not officially sanctioned (which means, basically ALL hardware drivers that were published before pretty recently), breaking all my software with new restrictions that were not in place when that software was published… it's all just a majorly huge pain in the behind, and while it's cool that they're doing that, they need to give users the option to disable that stuff if we upgrade so that we can still run all our old stuff without having it break.

Oh and let me add that having Apple Music and the "simplified, clarified" interface to iTunes (which did NOT need it) shoved down our throats was not appreciated easier. They should have made it a separate app and not built it into iTunes, which was ALREADY an insane piece of bloatware.

All very valid stuff but regard this from a money perspective.  That's what for-profit corporations do.  Is there money in the 5% of users who have demonstrated they only buy new hardware once a decade and who by their own admission don't have enough money to even upgrade software? Or are you just going to target the 95% of users who frankly don't want to have to think, or take into technical consideration anything more complicated than an on/off button, who can be lured by the 'fastest and most advanced' into spending a couple of thousand dollars every 4-5 years and who can afford that?