I love this little saying: Just because Lunch comes everyday after Breakfast does not mean that Breakfast causes Lunch.
In your case killing the apps may speed up your phone, but it is only because you have some flawed apps. Find the flawed apps and get rid of them. Others don't see the benefit of running a task killer because they do not have the flawed app(s) that you do. A task killer will not and did not speed up my phone, just as some people suggest rebooting everyday to speed up your phone. None of that works on my phone because I know the cause is bad apps and I search them down and get rid of them.
Edit: Oh wait, I thought of another one - using a Task Killer to speed up your phone is like putting a bandaid on a flea bite without getting rid of the fleas.
Let me clarify that I'm justing the app TasKiller, not just A task killer. I cannot vouch for what features the other ones provide. Also, the supposedly flawed apps you mention would be a little difficult for me to remove given they are the apps and processes that are on the phone by default. I'd assume the next idea is a factory reset; a solution I'd like to steer from as it seems awfully Blackberry-esque and I'd think Android is better than that.
Also given TasKiller is basically just a task manager, except with the ability to auto kill instead of manual, why would Android have it's own built-in task manager if it were never necessary to kill an app? Not to mention the TasKiller process itself can be killed so there goes the "Task Killers consume memory themselves." lecture.
The built in task manager kills apps when more memory is needed to run something you've requested. It is a waste of your time and system resources to kill apps that are going to be restarted by the OS. They are not "running" in the same sense that programs are running in windows. They are parked, drawing no power and using no cpu cycles, in memory waiting to be used.
Lastly, in Windows, if I pull up Mozilla Firefox, it begins consuming memory. As it remains open, it consumes more and more memory, and this becomes noticeable. However in Windows I can simply close Firefox, reopen it and start fresh. On Android, when you exit the Browser, it never ends the process, meaning the resources it has consumed running are being wasted now that you're not using it. What is my solution in this scenario?
As stated above concerning the difference between Android and Windows is that in Android a program in memory is not using power or cpu cycles.