Hmm. I've had two ASI failures, and zero tach failures.
Anyone should be able to fly a reasonably speed-consistent pattern in an airplane they're familiar with, without looking inside at anything.
Must get in touch with your ears, butt, and control feel, grasshopper. (And if you aren't trimmed to fly hands off, you'll never notice if the controls are sloppy and you're slow, or tight and you're fast...)
Get a few hours in a glider and your ears will be in the game. Big time.
Get a few hours in a taildragger and your feet will be in the game too, of course.
I set power by numbers for gross changes because I know what speed it will end up at -- after the airplane decelerates -- if all is nominal.
In an airplane I know well in the pattern? Looking outside mostly.
You can hear and feel it getting slow or fast.
I cross check occasionally against the ASI for target speeds in each leg of the pattern. In the 182 it's 85 downwind at descent, 75 base, 65 final, 55 once over the fence. Four glances at ASI. Don't really need anything more.
One power adjustment to start down, one more on short final. That's usually all that's needed if I fly the pattern correctly.
No need to make it difficult though. Look outside, "fly the airplane normally while descending and slowing a bit" is really all you're doing for downwind descent, base, and turning final. Don't make it into rocket science in your head.
Final to landing, you're operating nearer to limits as you continue to slow so a peek or three at the ASI isn't going to hurt. But again, it really shouldn't be all that necessary.
Now in the twin it has to be fly-by-numbers, because there are some flight speeds you can get yourself into that really you shouldn't be at. I have a feel for the sound and butt and control feel thing in it now, but you really need to watch and use some known power setting numbers anyway to alleviate setting up a bad trend.