You're right that unions overplayed their hands, the problem is that so many of them are still living in the past and are still overplaying them now. There is little public sympathy for unions that inconvenience them, and so they will find it increasingly difficult to use their disgusting ransom tactics to hold employers over a barrel.
Again, market forces rule. Those with rare skills are not finding those problems.
I'm not sure where this idea that workers have a certain level of worth regardless of education and/or ability comes from. As with any market, rare and desirable assets will have value, commodities that are easily found/replaced do not. Society is changing, and people need to change with it. There is a problem with our education system, it doesn't properly prepare people for life outside of school and it really needs to. Good teachers can spot those not suited to academia - those people should be learning trades that they can use when leaving school, not being prepped for college where they'll take any old course because that's what the government thinks they should do. Many are even shepherded into university to waste another 3 years on subjects that will do them no good in the longer term.
But school issues aside, there are plenty of opportunities to expand one's knowledge - I have a couple of employees working for me who changed their careers later in life and they're being well rewarded for it.
1) To my mind, the unions have been punished for their hubris in the 1970's - unlike in the 1970's (when 'Beer and sandwiches at Number 10' was the ever-present sneer), the unions today are nearly powerless compared to their previous incarnations. Their tactics are the same, time-tested tactics they have used for a century and a half to help their members and the working class against the inordinate power of their employers- but if the public *still* dislikes them using these tactics even when they are as powerless as they now are, then that can't be helped, because giving up on the right to strike would be invalidating their purpose as unions meant to serve the Average Joe, not the employer who would love for that Average Joe to be atomized and unable to negotiate with his employer in anything more than the most superficial bargaining position.
2) 'Rare' skills are rare for a reason. They cease to become rare if everyone is capable of acquiring them, and then you are left in the same situation as you were before you sent everyone away to acquire these skills. Again, that is not a reason for those without those skills (the vast majority in nearly every high-skill/low-skill society in human history) to meekly submit to having their power and rights relative to their employers stripped away because an infinitesmally few people in the golden tower get to negotiate on more even terms, so it's clearly 'working fine for everyone else too' without the need for unions.
3) The idea that workers have a certain level of worth regardless of education or ability comes from the humanist belief that people have an intrinsic worth as human beings, allied with the assurances that generation after generation of governments have given to people (the world over) that there is a fairly-won place for them in society if they work to the best of their abilities, whatever their role and economic status. If you don't like the idea that low-skilled people want to be treated fairly and won't keep schtum when they feel ill-treated (and won't just conveniently leave their positions), then you have a lot of work to do to undo centuries of humanistic thought in education, government, law and wider society - you'll also need to bluntly tell people that they only matter if they have a skill the market deems necessary. You could create this fantastic free market paradise this way, of course - but don't expect it to last very long, because the first person who argues for more fairness outside of the GHod of 'market forces' poses an existential challenge to that order.
4) Universities were *never* meant to be job skill centers. They were meant to teach young people to think, criticize, evaluate, argue and question - to test the fundamentals of their world in an environment outside the rigid confines of the school system. Their purpose was to educate and to (most importantly) *research* the world while doing so.
Job skilling was meant to be the province of the companies who hired people to do those jobs. Somewhere along the line, the companies themselves made it their goal to dispose of that unnecessary expense in favor of telling the universities to turn into job-training centres, because they couldn't be *rsed an would rather rid themselves of that expense. Now, our graduates are the most educated any generation has ever been - the most intelligent, the most inquisitive, the most widely read. And yet, they are also part of the generation that is bluntly being told not to expect to live lives as good as those of their parents, by the very cohorts who (in some cases) didn't even need degrees of any sort to get into the jobs that they presently employ.
It isn't a problem with the West's education system - it is definitely a problem with the West's corporate world privatizing profits and socializing costs. (I exclude Germany from this statement, because in many ways they're a symbol for the West to follow in terms of labour relations, job training, apprenticeship programs and corporate responsibility).
It is if you're really good at what you do or are particularly hard working.
Those employees that have left us over the past decade or so were mainly ones that we were not so fussed about losing. We've done everything in our power to keep and progress the good ones because they hold extra value to us. I don't think my company is unique, or even rare in that regard.
Very few people are really good at doing things the market deems 'valuable' enough to place on an equal bargaining position relative to their employers.
Many people are good at doing things the market doesn't deem valuable enough to be worth anything substantial.
Many, many people are very hardworking, often working odd hours and multiple jobs just to make ends meet.
The market is not fair, in any way, sense or form, given these realities. What its caprice deems profitable, it will prioritize (And people lucky enough and talented enough to be good at doing something within that field will profit from it). Otherwise, people are SOL.
This is why unions were formed. Not for the benefit of the 2/100 people who were lucky enough to be good at something the market deemed worthy enough to remunerate well and treat fairly. But for the other 98/100 people who were (in the main) ordinary, reasonable hardworking folks who just wanted a fair slice of the pie and dignity in their labour and in their lives.
Your suggestions are all based on the idea that the privileged few enjoy negotiating power secure enough to command their wages and working conditions, so it's all fine. That model only works for that privileged few - literally no one else has been served by such a laissez faire system without the social and governmental safeguards afforded by unions and humanistic governments. Safeguards which came with a lot of blood, sweat and tears, wrested from the hands of often unwilling employers.
Safeguards which, when not provided in some cases, led to bloodshed and misery when the dam burst.