My experience has been that departments control documents applicable to their area. For example, a laboratory (let's say the laboratory manager) would have a listing (at the very least) of the equipment manuals they had. I've seen the equipment manual and its location put into comments of calibration software which is a means of control.
Same with production. For example, let's say you have a turnkey design and build a line. You do runoffs at their facility and then again at install. The turnkey gets manuals for things they buy for the line. Those manuals should be included in the turnkey's master manual. The master manuals from the turnkey give source and part numbers for motors, servos, transmitters or whatever, including those from suppliers. Those manuals are critical to maintenance, thus they should be closely controlled, even revision wise. I was in one company which had a machine that had a simple timer motor. The original motor failed rather regularly, as in once or twice a year. Maintenance found a motor guaranteed for 10 years. They updated the line manual to reflect this.
But - Even at home I'm a document nut. I have a couple of file drawers that have manuals, warranty certs, sales receipts, and all that stuff for everything I buy from my chipper to my dish washer. I use plastic 'folders' with the ties a lot. I admit I don't keep a listing such as a spreadsheet, but I can go through my files and find every manual for everything. I do use folder indexing such as 'bathroom' or 'roof' or 'kitchen' or 'yard', etc.
Last year I paid US$5 for shipping for a Price Pfister 'lifetime guaranteed' kitchen sink faucet replacement that was 12 years old. I had my receipt, the guarantee and all that.
In any company, if departments are not controlling essential equipment manuals, it becomes a cost/waste issue. I have seen quite a few discussion threads here where the person was looking for a manual for some type of equipment they had.
There are a number of 'manual' web sites out there that charge for equipment manuals which you can no longer get from the manufacturer. This also accentuates that not keeping and controlling equipment manuals is a cost issue.