1) Could you provide an argument for the thesis that all culturally induced behaviours* need to be fixed? ...
*As opposed to only harmful ones, like wife-burning and homophobia.
Define harmful for me.
Your examples suggest that you find both direct, physically harmful and systematic discrimination and prejudice 'harmful'. Surely it's not a huge leap to see that cultural induced behaviours that re-enforce sexist ideas and views of women are harmful in this latter sense?
The stereotyped assumptions that women can't cope and don't want to carry out traditionally male jobs for whatever reasons are explicitly harmful to the women who can cope and do want to enter those fields. The idea that certain fields should be accepted as boy's clubs because of some unsupported assumption about the average woman is one of the factors that keeps these fields boy's clubs.
As far as physical labour goes, there seems to be a double standard. Traditional physical labour jobs are still heavily male dominated, even if they are relatively minimal as far as strength requirements go (hell, I've done a primarily physical labour job when I was heavily out of shape). More recent jobs with substantial physical components, or components not always recognised as physical, often trend female.
Compare the work I did at Parcelforce (heavily male gendered) to a woman working at
Amazon in a warehouse. My job was in a traditional, heavily unionised industry with dozens of safety and health regulations. There were limits on the weights we could lift, even if they were occasionally ignored. We generally asked for and got help lifting anything particularly heavy (unless wanting to show off), and the majority of particularly heavy items were labelled correctly. There were frequent breaks throughout a shift, generally determined by the natural work flow but enforced by management if no gaps appeared. Shift managers were generally on the line with everyone else. Protective clothing was required and could be supplied if needed. While women were drivers, none worked in the warehouse as that was seen as a physical job. Most of the physical labour was moving objects between a (height and length adjustable) boom and cages or piles on the ground/truck, maybe carrying them for two or three steps. There were some time pressures when unloading trucks, but often the loaders (easily most physically demanding part, which I was generally dumped into as a short term temp) were going too fast for the sorters down the line.
Amazon pickers do much the same thing (although maybe with fewer packages that exceed the 10-20kg range; we handled Amazon packages and they were generally single books/dvds, but there were frequent heavier exceptions) except the heights they are picking objects from are, by all accounts, not controlled. They also have far fewer breaks and have to walk far, far further. According to reports their safety equipment supplied was insufficient for the demands of the job, if present at all. There doesn't seem to have been any real assumptions either from the employers or employees as to whether it's a job for men or women, and the early articles I saw about it were a rough split in complaints about conditions from men and women.
Now I've known dozens of women who were more than capable of carrying out the Parcelforce job. I don't imagine that any of them would apply for or get such work, even if unemployed and in need of money. At the same time the Amazon job sounds far more demanding and physically damaging. A decent chunk of that is the lack of regulation and safety requirements, but the general layout of the job (walking to collect shelved items) is likely to be inherently more exhausting than the work I did. Given the choice I'd probably sign back up at Parcelforce over doing the Amazon work, as that sort of labour builds strength better than reaching and excess walking. Anyone, male or female, who managed that Amazon work could easily do 99% of the Parcelforce work, and certainly anything that some of the younger guys (we had 16 year olds working there at times...) could manage. The differences seem to be entirely attitudes towards the job and established workforce, which kinda shits on the people who aren't accepted into the frankly safer work.