It's not orthogonal. If you look at societies that industrialized early, their social development diverged hundreds of years before industrialization actually happened. When my dad was born in 1951, 90% of the population of Bangladesh lived in villages in extended kinship networks and multi-generational households. In such an environment, the informal rules of families dominate society. Bangladeshis have a very relaxed attitude towards time and rules. It's not a big deal if you're late in my dad's village, because everyone knows you and that you'll arrive an hour or two after the official time and will plan accordingly. If you inconvenience someone, it's not a big deal, because you're all family and you'll reciprocate the accommodation another time. (That's a key point! Kinship bonds form a kind of collateral that ensures that accommodations will be reciprocated in the future.) Plus, the country is blessed with three growing seasons, so nobody is in a hurry anyway! And if you're persistently causing problems, it will percolate to higher ups within the families and they'll set you straight through informal processes.

Contrast somewhere like England, where, for whatever reason, extended family networks began breaking down as far back as the middle ages. People in England were living in small nuclear family units back in the 14th century. When your neighbors aren't related to you, that forces people to rely on formal rules and procedures. You can't count on future reciprocity backed by the collateral of kinship ties. And if someone is causing problems, you need formal systems, based on rules and procedures, to deal with them.

These formalized systems are, in turn, far more scalable! You can plan and organize civilization building when everyone is socialized to follow formal timetables in a way that you cannot when people are socialized to follow the informal timing consensus. And the lack of individual accommodation is a feature when you scale from small networks of a dozen or so related individual to millions of people moving through the London Tube every day.

A small amount of rule breaking is tolerable, even beneficial, within a society where everyone otherwise rigidly adheres to rules.[1] But there is no developed society that isn't rule-based at the baseline level. In some places, like England, this rule-focused culture developed organically. In other places, like Japan, there was a deliberate effort to destroy extended family networks and clan structures and replace those frameworks with systems of formal rules and procedures.

[1] America is a good example of a society that is less rules-oriented than say Japan, and arguably derives some benefits from that. But even in America, we pay a price for that. Americans just aren't as good at large scale social organization as the Japanese or Taiwanese, and we compensate by structuring our society in a more decentralized way where less such organization is required in the first place. Ronny Chieng has a funny bit about how New Yorkers try to force open subway doors that have already closed: https://www.youtube.com/watch?v=ifX0oafDe3Q. This behavior, multiplied by thousands of occurrences per day, slows down the whole system.