What are the fields in which the return on investment of learning a skill and DIY typically exceeds just relying on the division of labour society?
According to economics, it should be the case that one should practice specialization. That is in fact how we have our wealth as we moved from a barter economy to an economy with money/currency. The division of labour was able to develop and efficiency as well as gains in specialized fields of knowledge were able to be obtained. For example, a barter economy cannot sustain a particle physicist because he cannot trade his effort directly for the goods he needs to support his life, without money and the division of labour. The existence of money allowed the division of labour to develop, and thus more and more specialized fields of work.
However, we do not live in a perfect division of labour society, which would imply laissez faire capitalism. There are enormous government imposed barriers to entry in many fields, especially those of skilled labour because of licencing laws and trade groups which lobby the government to restrict competition so they may keep their hourly rates high. Another important factor are the immigration laws, which restrict the free flow of the movement of labour from willing buyers.
I can sympathize with Jacobs position on DIY because I think he originally came from Denmark where the medieval "guild" is still in tact, with unions and the government on one side bidding up the wages of some fields while restricting entry of labourers into them. On the other hand, many people in America can hire a Mexican gardener or repair man at much lower rates than they will earn from their specialized income.
This is the reason why I outsource a lot of common activities that Americans do themselves, while I am in Asia. For example, the minimum wage laws and building codes are almost non-existent in many Asian countries. If an old grandmother who has a great kimchi-soup recipe wants to open a restaurant, she puts some plastic tables and chairs into a small space, rents it out, and begins business. She does not have to build a 1.5 million dollar building up to code. She does not get shut down if she does not have a large handicapped bathroom stall. She does not have to do $50,000 in upgrades if she is missing a handicapped bathroom stall. So, in the case of many Asian countries, the barriers to entry for opening a restaurant are very small. In North America, one needs to get a loan of tens of thousands of dollars to open a restaurant. The barriers to entry imposed by the government are high, thus destroying some of the advantages of the division of labour society and making self reliance more important.
Now, we live in the society we live in. Taking our society at face value, what skills should one learn that provide the highest return on investment? Keep in mind that we have to spend time learning these skills first before we are able to implement them. So we should factor in the opportunity cost of learning the skill plus practicing it, compared to performing in the market at our specialty and average hourly wage.
There are arguments to be made that the quality you can obtain from making something yourself is superior than the market offers, because most people in the market are uneducated or do not place emphasis on that particular quality, but I would like to stay away from that argument as much as possible in this thread in order to keep things uncomplicated. An example of this is saying, "I can produce eggs that have higher levels of vitamin A, D, K2, and omega-3 because the chickens are allowed to walk around and eat their evolved diet of grass and bugs rather than nutrient deficient grain feed in a black warehouse." That's true, but for simplicity it might be better to compare the same product (DIY) to same product (market obtained).