A motor has to be running in an under-voltage condition to get unhappy, and it takes a while. In that condition, the motor overheats which takes time. Hard to say how long, could be 5 minutes or more. If the dryer was not running but just plugged in, it's not under voltage and is more likely a big honking spike.
Even with my whole house protection, I have a "rule" that nothing other than a light bulb is plugged into a socket without a protecting plug strip. Generally speaking, there are two flavors of plug strips. The simpler and lower cost ones just have "spike protection" in them. The device just has MOVs in it. Then there are more expensive versions that have filters in them. The filters are low pass filters which means then block the passing of high frequency energy. If you recall, lightning noise is high frequency. The spikes you get when motors turn on and off are high frequency. So the filtering strips utilize both the high frequency filtering and MOVs to protect what's plugged into them.
The slow degradation of electronic devices due to spikes is not a myth. We're back to those nasty high frequency spikes. They can couple through the power supply components and into the electronics. They also slowly strain a number of parts in the power supply (diodes and capacitors) hastening their inevitable failure. The good new is that this problem is getting to be less of a problem with almost all modern devices. The power supplies in just about all electronics (computers, TVs, chargers) use a circuit called a switching power supply. This circuit produces a lot of high frequency noise (stuff that gets in your radio and TV). So these devices have filters on the AC power line input to keep the noise from getting out so they can meet the FCC emissions specifications. Well, the same filter that keeps the high frequency noise from getting out helps attenuate the high frequency spikes getting in.
So this whole business of protecting electronics is much like the problem of storming a medieval castle. The spikes have to clear a number of obstacles before they get in. First they have to clear the whole hose filter. Then the filtered plug strip. Then, the EMI (electromagnetic interference) filter on the device itself. All these things need a good ground so there is somewhere to dump the energy.
One more nice parasitic side effect of MOVs is they have a lot of capacitance to them. This helps eat high frequency energy too.
At story: At our old house, I had 9 ground rods. We had a very bad drought in 2003. I had a PBX phone switch at the house since it was built in 1988. During that dry summer, we had a bad storm. I lost the PBX. We had plenty of bad storms before, but the dry conditions affected the ground quality. No problems with anything before or after that. Our neighbor across the street and on the same transformer was always loosing stuff. So it was an interesting test case for the "gauntlet of protection" I had.
The ground system also helps the telephone company's gas tube protectors work better. I don't know if I lost the PBX to an AC spike or a telco spike.
Protecting AC is very different from protecting "information" wiring like telephone, driveway sensors, and coaxes. But all protection circuits need a good ground. Information stuff is easier to protect because the wires are smaller (so they get more voltage drop on them when they get hit) and you can introduce some loss (resistance) into the scheme with no problems. But I'll stay on topic with AC power protection.
As for protection of low voltage, the only devices I know that do that are transfer switches for generators and UPS like you use on computers. I have a big honking UPS in the house and every computer and TV is on it. The little ones you can by at the box stores will switch over when the input voltage is high or low. There is no economical solution for the big motor loads of your house, like compressors and fans. It would be really nice if the manufactures build sensing and cut-off circuits into these devices, but since so few people understand this stuff no one would be willing to pay for it.
As with all types of protection (power, lightning, fire, security, etc) the absolute last "stage" of protection is insurance. And you also have to realize that like many points in you life, sometimes despite your best efforts and preparations you're gonna get kicked and you just have to own it, not expect someone else to pay for random back luck, fix it on your own and continue onward. Ooops, got a little philosophical there

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Pete