Obviously the OS is consuming more memory for internal tasks, but why exactly?
Newer versions of software is developed for and tested on newer hardware, which is more capable. So they will not see that issue. My speculation: Apple does not bother to optimize for older devices because their culture is very focused on the future.
Is this a strategy from Apple?
Nobody knows unless they work for Apple, in which case they would not tell you.
If other people are not seeing these results, what should I be looking at?
My friend has an iPhone 4 and the performance is okay, even though there are some hiccups in animations. If you absolutely cannot stand the bad performance, consider doing a clean install or buying a new iPhone.
P.S.: I have more than 2GB free space
Your bottleneck is probably not having enough RAM, forcing the OS to send memory warnings, purge apps from memory, and reload them from disk.
and I keep the background clear of apps more than a few times per day.
Force quitting your apps actually reduces performance: http://speirs.org/blog/2012/1/2/misconceptions-about-ios-multitasking.html