Teknetics, Tesoro or White's, I never use a coil cover. Coils are not supposed to be scrubbed on the ground as the Owner's Manuals generally suggest working them anywhere from 1" to 2" off the ground. Due to the high gain used with most detectors these days, the coil should have a proper coil-to-ground gap to help eliminate swamping or warping the EMF with close-proximity high ground mineral. Also, if worked on the ground, that causes drag which leads to fatigue, and also leads to an interrupted or uneven search coil sweep presentation.
If I ever get a detector coil that comes standard with a coil cover, such as my Makro and Nokta models, then I leave those thin, light-weight covers on until I have a need to remove them .... then they stay off. Over fifty years of very avid detecting and I have never worn out a search coil, or had an issue with any coil caused by not using a coil cover. Coil covers, although they seem light, add extra weight out on the end of that rod and it can cause fatigue, even with a smaller size search coil. Work a search coil over an area for maybe 30 minutes with a coil cover on. Then pause, remove the coil cover, and hunt another 30 minutes. It won't take more than a minute or two for you to notice the much better 'feel' and balance of the detector using he very same search coil, but w/o the cover.
Monte