Diffused strips or bare LEDs - which camp are you in?

I fought the same battle a couple years back with a strip behind our TV console and ended up putting everything in aluminum channels with the milky cover, and I have zero regrets. Before the covers, my wife called it the dot effect and refused to watch movies with it on. After, it reads as one smooth glow and she actually asks me to turn it on now. The brightness loss is real but you just bump the power up a notch and it's fine. The trick nobody tells you upfront is that the channel needs to be far enough from the surface behind it. I first mounted mine tight against the wall and still got that harsh bright line right where the strip sat. Pulling it out a few inches, even with simple spacers, is what actually spreads the light. Distance matters more than the diffuser itself for killing hotspots.

For the bookshelf specifically, bare LEDs tucked under a lip where you can't see them directly is honestly fine, that's where I left mine naked. But anywhere at eye level, like behind a headboard where you're lying in bed staring at it, the frosted cover earns its money. On the second room I'd buy the channel from the start instead of redoing it like I did. One other thing, get the cover in a longer length than you think you need, the corners and ends are where I came up short and had to splice ugly.

For my project under the kitchen cabinets, I went the bare strip route initially, because I wanted the colors to pop when I ran the WLED effects. My main concern was the intensity, not the dots themselves. The light bleeding and individual LED points were noticeable at low brightness, but once I pushed the brightness past 50%, the dots just merged into a continuous band of light anyway. My wife initially complained about the scattered light, but once we were cooking and the mood lighting came on, she stopped noticing it.

If you're worried about the 'dot effect' killing the look, maybe the issue isn't the strip itself but the mounting surface. I found that if you mount the strips a little further away from the wall, maybe an inch or two, it creates a slight gap that helps soften the harsh edges of the individual LEDs, rather than having them flush against the plaster. Instead of jumping straight into frosted aluminum channels, wich adds a lot of bulk and inevitably reduces the saturation of the colors, I tried covering just the front edge with a very thin, milky acrylic diffuser sheet. This didn't hide the dots completly, but it took the harshness out of the white light and gave it a more uniform glow, without totally washing out the saturated colors I was aiming for.

Before you buy anything, try the cheap test first. I taped some tracing paper over a strip once just to see what a diffuser would look like, and that told me everthing. You can do the same with a strip of white plastic cut from a milk jug if you're broke and curious.

Also worth considering, higher density strips fix the dot problem without a channel at all. My bedroom one has way more LEDs per meter than my old strip and it looks smooth even bare. Costs a bit more up front but skips the whole mounting hassle.

For the headboard specifically, how far off the wall are they sitting right now?

Back when all we had was dumb 12v ribbon and wall warts, I used to slide the strip into a length of white PVC conduit with a slot cut down one side. Crude but it worked, and honestly the aluminum channel stuff today is just a fancier version of the same idea. One thing I'd add on the headboard part: think about where your eyes sit when the lights are on. Lying down changes the viewing angle completely, and a cover that looks fine standing up can still show dots from a low angle. Test it at night from the pillow before you commit to anything on the second room.

On the washing-out worry, from my own setup the frosted covers do mute the colors somewhat, saturated reds and blues that pop on a bare strip come through the plastic looking softer and slightly milky, which is precisely the trade you are making for smoothness. One thing that helped me with the low-brightness dots before I ever added a cover was simply not running the strip in the bottom range of the dimming, since that is where each LED is most visibly its own point of light, and keeping the slider above a certain floor made bare strips tolerable in our hallway. Might be worth testing that on your existing install before buying anything, since it costs nothing and tells you quickly whether the dots bother you at normal viewing levels or only at the dim settings your wife is complaining about.

Update: I ended up going with the aluminum channels and a frosted cover. Just like one person suggested, the difference was huge. It totally removes the dot effect that was bothering my wife. It makes the light feel much smoother and higher quality, and I have zero regrets on the upgrade!