That's the spirit!

If you don't have a sensor then that is cheaper in the short term, but it quickly wastes a lot of energy running when the humidity is under control. For a dehumidifier you need more energy to get lower so the room well generally will be fairly consistent not too low humidity even as outside humidity changes, but you will use a lot more energy than a system that turns off when humidity is good.

there are purely mechanical systems that used to be used. However they have some weird machining requirements so it isn't clear they are cheaper than a digital system (this partially depends on volume - make more and the machining gets cheaper per unit). The digital system is as we already have established is very cheap and lets you put buttons and LEDs on the unit for a few cents more - this is far more valuable to marketing than the possible savings (if any!) from a mechanical control.

Again, I’m not sure what components were used in the older model, but given the age I’d be very surprised if the electronics it uses would be more expensive to manufacture than the newer one.

That's fundamentally where you're going wrong, then. 1980s electronics (for a dehumidifier, it wouldn't even be electronics, it'd be electromechanical) are often much more expensive than modern approaches, and even when they're cheaper, it's typically not by much. Over time, it's got cheaper and cheaper to precisely make small things, but the costs of materials haven't meaningfully gone down, so the 1980s approach costs about the same as it did back then, whereas digital electronics have plummeted in cost. Now, anything where the best approach was electromechanical rather than electronic is almost certainly cheaper to do digitally.

Take toasters for example, most toasters don’t have a timer at all. They have a little piece of metal almost touching a contact. When you turn the toaster on, that metal heats up and it bends until it touches that contact, ding toast is done.

Another great example of being out of date. Fifteen years ago, cheap toasters almost always used a bimetallic strip and the dial controlled the position of the contact it touched so it would have to bend more or less before it disconnected. In nearly every modern toaster, however, you'll either have something like a 555 timer and the dial will control a variable capacitor that changes the frequency of an oscillator to make it count slower or faster, or it'll have a dedicated toaster control chip like the BCT5512 and the dial will control a potentiometer that a capacitor drains through. Mouser list the PT8A2511PE toaster controller for £0.111 in bulk, but the cheapest bimetallic switch they carry (which is too basic for a toaster because it's got a fixed switching temperature) is the F13A17005L360100, which is £1.93 in bulk, more than seventeen times the price. (I suspect they used to have cheaper ones back when toasters still used them, and they've been discontinued now toaster manufacturers have stopped ordering them.)

But it’s cheaper and simpler to just do it the old way, and for many applications, that’s fine.

A lot of the time, the old way is more complicated and more expensive. Technology doesn't just let us do things we couldn't before, it also lets us do existing things in new, better ways, and being cheap is one of the most in-demand things. It's lower tech to hire ten labourers with shovels for a week to dig a hole, but it's much cheaper and faster to hire one labourer with a digger to dig it in an hour.

Hell, I’m certain there are dehumidifiers on the market that don’t have any kind of humidity sensor at all. Even simpler…

Having no sensor at all is certainly the cheapest way to do it, but we were talking about ones that do have a sensor, and whether, once you've opted to have a sensor, there's any major cost to making the device smart. If you're aiming so low-end that you don't even have a sensor, then you're clearly not concerned about the marketing benefit of extra features, so wouldn't bother making it smart.

So you think the reason a hygrometer can't detect humidity ten minutes before it exists in order to start cooling the dehumidifier's compressor to the temperature it needs to be to start working is human error?