Effects that occur to me:
One: As yo mention -- so let's deal with that right off the bat -- in many cultures it is advantageous to have sons. In China, the custom is that your sons provide for you when you get old. Your daughter doesn't: she'll be working to support her husband's parents, not her own. So if you don't have a son, you can never retire. You have to work until the day you die. In India, the parents of a girl are expected to pay a large dowry to her husband and his family when she marries. I think it's much less of an issue in Western cultures, but still, fathers often want to have a son to carry on the family business. In general, it is sons who carry on the family name. Etc.
So if you're going to make this work, you have to someone bring about social changes so that baby girls are equally desirable. It's easy to describe social changes that would make this work. Getting people to actually accept them is another story. And, I might add, it's easy for some technocrat sitting in his office to dream up social or economic change that he thinks will be an improvement. But putting it into practice often brings up all sorts of issues that he never considered.
Two: You also mentioned supporting the elderly. Yup, that's another problem. In the U.S., social security was originally designed when there were, well, in a quick search I couldn't find the numbers when it started, but in the 1950s there were 16 people paying in for every 1 receiving benefits. Today it's less than 3 to 1 and falling. Taxes to support it have risen from 2% to 12.4%. With a declining population, you'd have to either force people to retire at older ages or increase taxes even more. At some point the burden on the young becomes unsustainable. This of course applies whether you rely on a system like social security, the young person directly supporting his parents, or any other system. The money to support the retirees has to come from somewhere.
Three: Economic diversity. As technology advances, people become more specialized. A couple of thousand years ago most people were very literally self-sufficient. Most people were farmers, and a farmer built his own house, made his own tools, then used those tools to grow his own food, etc. But as the economy becomes more complex, people specialize. I develop software for a living. I have never made more than minimal efforts to grow my own food -- a few attempts at a vegetable garden -- and those have been total failures. I have no idea how to build a house, or 90% of the other things I use every day. Even farmers today aren't self-sufficient. They don't build their own tractors and drill for oil to run them, etc.
If the population is shrinking, it becomes more difficult for people to specialize. Sure, there are enough store clerks in the world that if population was cut by 80%, we could say fine, there will now be 80% fewer store clerks. But some jobs are specialized enough that there aren't millions of them in the world. If we cut population by 80%, can we just cut the number of coal slurry pipeline workers by 80%, and have the system still work? The number of agronomists? Etc.
Three: Some things only work on a sufficiently large scale. If the population was reduced by 80%, presumably we wouldn't need as many roads. But could we abandon 80% of the roads? Not if we still want to be able to travel around like we do today. Could we abandon 80% of the cell phone towers? Not without losing coverage to large areas. Etc.
Four: How do you manage the depopulation? I live near Detroit, a city that has lost 60% of its population since its peak in the 1950s. This has caused huge problems. For example, there are now neighborhoods that used to have hundreds of people, but now only 1 or 2 houses are still occupied. How do you continue to provide utilities to those 1 or 2 families? Miles of water pipe and power lines and phone lines were built with the intent that they would support hundreds of customers. Now the maintenance cost is almost the same but they are supplying 1. Who pays for that? In some cases the city has paid people to move out of abandoned areas just so that they can shut off the utilities and stop maintaining the infrastructure. People find themselves living in areas where all the houses around them are abandoned and slowly decaying. Crime is rising. Wild dogs and other animals are becoming a problem. Etc.
Five: Science and technology advance through the contributions of a small number of geniuses. But we all benefit. For example, the microwave oven was basically invented by one person, Percy Spencer. I don't know how many microwave ovens have been produced since then, but say it was one billion. How many people would it have taken to invent it if two billion had been made? Or only one million? Clearly the answer is, Still just one inventor. It doesn't matter how many people benefit from his invention, the work and creativity to invent it are the same. If you double the population, then all else being equal you should have twice as many inventors. But the benefit to the average person for each invention is not halved because there are twice as many people. It's the same. So the more scientists and inventors, the more we all benefit. Cut the population by 80%, and presumably there will be 80% fewer scientists and inventors. Scientific and technological progress will slow by 80%.