Sorry to disagree, but I feel like the last bit of your post is possibly just a standard trope that people parrot back.
Have you actually tried to get a HGV license like I have so that you actually know what the recruiting process is? Or learnt a trade? I'm not convinced most of the people who confidently state how hard it is have any idea tbh.
There's not really a 'recruiting process'. You take your lessons then you book your test. The test is much less subjective than getting job qualifications based on soft skills, because it doesn't come down to the 'perception' of the examiner to any large extent. Either you hit a kerb/check your mirror or you don't.
When on the job it's pretty evident who can do it well or not. The driver who rarely bumps into things and gets there on time is a good driver. The bricklayer who lays bricks neatly is a good bricklayer. The end product speaks for itself.
I spent quite a few years in bid/project management and it was much worse. With big teams, the manager often has a birds eye view and the people that work hard but keep their head down can end up getting less recognition than those that make themselves heard and say the right things in meetings/suck up to the boss etc. The former are often women and the latter are often men IME. Plus there is also subconscious bias at play and male favouritism.
Nobody cares about this in the industry I work in. They just want the materials on time and the job done. If you do a good job then that's it. It's not about 'professional reputation' and jostling to be next in line for promotion. Yes, I encounter a few knuckle draggers and I hear some jokes that would never get past HR in most offices, but overall it's a much better environment for me than corporate jobs were.
Some will no doubt deny this and call me sexist, but I firmly believe that women are just less keen on the whole to get covered in mud and dust and to work in jobs where you can't look good/dress nicely like in an office. But there is a real black hole IMO where non-academic, often working class, women disappear into shitly paid retail jobs because they see no alternative.
Men don't suffer this problem as they can go into trades, and the average salary for trade work is £10k above the average salary earned by a graduate. Of course, there are ultimately less opportunities to earn a six figure salary in trades unless you start your own business, but you can be guaranteed a solid £40k+ with many as opposed to maybe being stuck in a £30k office job like many people are.
It always strikes me when I stop at a caf for coffee that it's nearly always women serving the coffee and always men who are on the other side of the counter as drivers/tradespeople etc. A senior female account executive is probably not going to want to drive a truck, but a woman who's not academic or perhaps not particularly interested in pursuing the education path could well be better off learning a trade or driving a wagon.
Driving arctics, for example, can easily pay £50k with a couple years experience and costs about a fraction of what a degree does. It's not a particularly dirty job compared to site work and despite the intimidating size of the vehicle it can be surprisingly easy as you mainly drive on the motorway/A roads and deliver to large depots which have plenty of room to navigate and big wide bays which you can reverse straight onto.
It might not appeal to the majority of women but I'd take a trade or hgv job over working in a caf or shop any day of the week.