Bureaucracies are the least responsive to complaints. If you are in your local DMV office to get your driver's license renewed, complaining will probably make things will worse. In many bureaucracies, the scarce input is time and attention. Within the constraints of the service process bureaucracies have created (which admittedly may be inefficient), dealing with complaints promptly, or even doing a favor, just isn't that easy.
Besides, as a state bureaucracy, the DMV is supposed to treat all customers equally. It's not going to say: "You've been a loyal state resident for 32 years, Mr. Smith, and you've been a good driver. So we've decided to give you an extra two years on your license renewal." Cases of DMV corruption are more likely to involve employees demanding bribes for truck-driver licenses than handing out favors to sweet-talking complainers.
Hospitals, and much of the health-care system, also tend to be bureaucratic, so complaining doesn't help much there, either. You are probably not the paying customer (most people have health insurance), and there is not much spare labor.
Contrast this experience with complaining at a hotel, which very often yields a relatively high return, whether your complaint is justified or not. If you tell the front desk that your room was not cleaned promptly and properly, or contact the hotel chain with a similar message, there is a good you will get an upgrade or extra points on your account. Most hotels have empty rooms most of the time, so they are not forgoing very much revenue by granting such favors. They might even be turning you into a more loyal customer.
The injustice you cite doesn't have to be that serious - what matters is that you brought it to their attention. That means you are looking for a benefit, perhaps with an exploitative motive, but still hotel management may respond. If you are a complainer by nature, you might also be especially likely to post on travel websites, and hotels want to prevent that.
The basic service and pricing model of hotels was never egalitarian to begin with, and that too makes it easier for them to give you a break. They usually charge different prices depending on the time and manner of booking - so if they cut you a special favor, no one looks askance.
The basic "economics of complaining" are becoming clear: Complain when the marginal cost of extra service is low. Complain when the reputation of the seller is evaluated online in a meaningful way. Complain when the service norms are something other than equal treatment.
How about complaining in restaurants? It works pretty often, but typically the rewards are not so high, perhaps a free dessert or drinks. The restaurant may be more interested in shutting you up than in cultivating your loyalty, perhaps because it knows you have so many options.
Complaining to the airlines is a tricky one. They often have free inventory to give away or offer at a discount, but unlike hotels, almost all their customers have something to complain about! (The same is often true of social media services.) Unless your case is strong and well-documented, airlines also tend to be pretty stingy about complaints.
As progress proceeds, and more services become automated and homogenized and well-functioning, businesses will resemble hotels more than airlines - at least from a complaining point of view. There will be fewer reasons for complaints, but the complaints that surface will be treated very well. Return on a complaint will be quite high, and if you (like me) do not love most complainers, you may find this slightly upsetting.
I haven't seen data, but in pandemic times the value of complaining has probably has gone up. Due to the collapse of tourism and travel, many sectors have lots of extra inventory. And with many businesses ailing, they may be especially conscious of their public image. But all these are also reasons that you, as a socially minded customer, should not complain so much.
What about complaining about the economics of complaining? The sad reality is this: Complaining is most lucrative precisely when and where it's needed least.
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