Tomna8r,
What actually happens if you don't 'clean the memory', I read you say it slows down, but what does the Activity Monitor show (screengrab RAM, CPU & Disk), do you see any orange at all in the Memory pressure graph, how about red? What is the process using the most RAM? How about CPU? Is that dedicated to one process?
There is a built in command that also purges. It may be safer than 3rd party tools (you already know my opinion on this 🙂). It's called 'purge' see if that is any different.
Have you tried Safe mode?
Hold shift after the chime until the spinning 'gear' appears. Ensure the login window says 'safe mode'.
https://support.apple.com/kb/HT1455
It will disable all third party extensions & startup items.
If the Mac is better in safe mode it is time to get a system report and look at the third party items. Be aware that some features will be disabled like wifi on some models, graphics drivers will be in a reduced mode - this is normal in safe mode.
Reboot to go back to normal.
How about another user account?
Create a new user account in 'System Preferences > Users & groups', give it the name test. Login as that test user & see if it works better.
YES indicates the problem may be inside your user account
NO indicates the problem may be further up in the system or third party software
It's clear you are dissatified with how it is behaving, are willing to try the tasks that might make it better?
It could just be a corrupted OS install (others have posted with apps that don't launch). A reinstall may resolve that, just backup & reinstall, it will overwrite the OS files.
If that doesn't help I'm afraid you might be right, but it's not what I am seeing with my 10.9 installations
P.S. Have a read of this you may see that 10MB of RAM free is not actually bad, compression will kick it as needed. http://arstechnica.com/apple/2013/10/os-x-10-9/17/#compressed-memory