Is it possible, that old smartphone becomes slow simply because it is old? I have 3.5 half year old Samsung / Google Galaxy Nexus i9250. The phone has become so slow after that time, that it is simply being unusable. Launching any application, as simple as Gmail or Calendar takes 2-3 seconds, sometimes even five. Pressing Home button needs 4-5 seconds between press and really showing up main screen of my launcher (Nova Prime).

When I purchased this phone, it was simply lightning fast.

I have about 50 applications installed, of which about half is used (15 from time to time and 10 daily) and the other half, never used or used once per 2-3 months. Because I change my attitude very rarely, I have installed these applications in 2012, when I purchased my phone and haven't installed anything or nearly anything ever since that. I would describe this as changing 1-2 application per year.

Because of above, I can hardly accept, that my phone is slow, because I installed too many applications during that 3.5 year period. We can assume, that I'm sitting on the same apps set for past 1-2 years. It is also hard for me to belive, that 50 apps, of which half is nearly never used is enough to visually reduce performance of such phone. Even though it is quite old, its hardware isn't that weak, as I assume.

I of course did a full factory reset once or twice, installing only the same set of applications, as in 2012, after that. It brought little or no help and little or no performance gain. This has actually "killed" me, because I was more than sure, that full factory reset will return this phone to a level of performance and speed close to the days, as it was brand new.

The only theory, that comes to my mind -- though very strange and unbelievable -- is that my battery is old, its performance is far lower than when it was brand new, and thus it powers all hardware with lesser voltage causing its overall performance to degrade.

I know, how stupidly this theory sounds, but it is the only one, I managed to come with, in given situation.

Assuming that number of installed applications and overall usage style of my phone hasn't changed over past 3.5 years of using it, is there any reasonable reason for why it is so extremely slower than it was, when it was brand new?
Performance has nothing to do with battery voltage. The reason is that the flash memory is "worn" and therefore slower and less responsive. 
My Nexus 7 (1st generation) is also very slow now and I have almost no apps on it. You can read more here: Why Android Phones Slow Down Over Time, part "No Solid-State Drive TRIM"


  No Solid-State Drive TRIM
  
  The lack of proper TRIM support was the main thing that caused
  Google’s original Nexus 7 tablet to slow down over time. This was
  fixed in Android 4.3, which added proper TRIM support. On Nexus
  devices, updating to Android 4.3 will fix this problem.
  
  If you have an older device that doesn’t have Android 4.3 and has
  slowed down over time, you can perform TRIM by rooting it and using
  the LagFix app. This app runs the same fstrim command Android 4.3 runs
  in the background. TRIM is necessary because of how solid-state drives
  work — solid-state drives slow down over time because flash memory
  cells must be cleared before they can be written to again. TRIM
  preemptively clears cells that contain data from deleted files,
  ensuring things will be as fast as possible when Android needs to
  write to those cells in the future.
  
  How to Fix It: Root your device and run LagFix if you’re using an
  older device. This happens automatically on devices running Android
  version 4.3 and newer.