I know this question was from last week, but I have an only slightly different angle that I'd like to share.
Android doesn't benefit from reinstallation in the same way that a PC does because it uses a different app model. A PC can slow down due to accumulation of useless junk files, plugins, and services running in the background that you no longer use. On Android, you can have junk apps, but Android does a good job of bringing them to your attention by requiring a notification while an app runs in the background or else the apps and services get heavily throttled to avoid using the CPU if the user doesn't access the app regularly. Android also provides clean removal of all files when you delete an application. Apps are very self-contained with few exceptions. If you removed all the apps you downloaded, the system is pretty much the same as its factory reset state.
In the really old days, a PC could slow down due to fragmentation of the files on the disc over years of use. This is no longer a significant problem because flash storage offers fast random access even to highly fragmented files. Manufacturers actually recommend against attempting to defragment this media.