This is a good discussion, there are already several different opinions - and all with good reasoning. Personally, I don't see the need for a wind speed indicator. I can tell the wind speed by the heel of the boat, the amount of weather helm and difficulty steering, the wave pattern, the wind on my face. Downwind, the speed of the boat, the difficulty steering, any hint of rounding up, the wind on your neck, the size of the waves ... all give you a pretty good idea of wind speed. I would never go out and drop a boat unit or two to be told what the wind is blowing.
I do however consider apparent wind angle a valuable tool. It is valuable at night, and when the wind is fluky. When I have a novice helmsman, I teach them about the telltales and steering to a far point and so on, but also tell them to use the apparent wind as a guide and keep it in the mid 30s say. It's an immediate sanity check for them. This is especially true at night for a novice helmsman, when they can easily become disoriented. I find it helpful for me as well, especially at night.
I grew up on a boat with nothing but a windex and telltales on the jib, and we won a Marion Bermuda Race. That windex on the mast is a beautiful thing. And while my instinct is to make do with less, I've gotten to appreciate the apparent wind reading and would miss it if it craps out. But I wouldn't rush out and spend a small fortune to replace it.
Look forward to other opinions; judging by the varied opinions you'll probably be more confused than before you asked the question