I have been working with PC’s for a long time and I have been compressing files through disk cleanup with no problems at all. When I re-format a machine I also have no problems. I would recommend you do this on a regular basis to keep your machine operational and responsive.
Compression does have some overhead to it, so it can at times slow your system down. Especially if you compress a file that is highly used by either a read or write process— for example IIS log files, SQL MDF/LDF datafiles, or Exchange database files.
Also keep in mind, once it’s compressed— it’s compressed, so you can’t compress it more. Additionally, compression on the disk does very little for already compressed files like zips, jpgs, etc.
File compression is specifically designed to save disk space or free up extra space on your hard disk drive. There is nothing wrong with compressing your hard disk drive as long as you will use it just for compression purposes.