What about the disclaimer of warranty and limitation of liability?

Disclaimer and limitation of liability is a very old legal aspect about trade law which from a US perspective historically originate from UK law before the time of colonization. It has nothing to do with copyright or technology.

As the story go, someone bought a mill shaft but the delivery was delayed and the customer sued the seller and wanted compensation for the delay. This in turn lead to a legal requirement to make the customer aware of limitations. When the US organization for trade (a name which is escaping me) made their recommendation based on the version of law which was "copied" over, they added that one way to do so could be to use all caps or by changing the color or font, which companies adapted by simply picking the first suggestion.

The distance of the original case of the mill shaft and some open source software thats public available on the Internet for free is quite a far one.

OK, but so what? It still in some sense restricts the rights of the person using the software.

Its not about software, so no, it does not restricts the rights of the person using the software. It restricts the right of the consumer who are in a consumer-seller relation.

Disclaimers are about what the buyer can except and have a right to after a transaction. The product in question is more or less irrelevant, through some laws in some places do consider a free gift to also be a transaction between consumer and seller but with a price of zero. This makes the law more complicated. For example, if a baker gives out free bread samples but that happens to be bad, the baker can still be held liable. However if I give a friend a home made cookie the law could easily treat the two cases in a very different way. As much with the law it depend on the situation and the details and the expectations of everyone involved.

This is in part why some open source project do not include disclaimers. They don't consider themselves to be in a consumer-seller relation with anyone and thus do not need to disclaim any consumer expectation which could occur if there were such relation. Some lawyers disagree with doing so because of the baker example above, through there is a lot of uncertainty and a lawyers job is to consider all possible bad outcomes even those that are unlikely to happen, or as it is to my knowledge in this case, never have happened to any open source developer in the world.

In what sense? You can still use the software, you just can't expect its use to yield a particular result and sue the programmer if it doesn't live up to that expectation.

In exactly the sense you just stated.

That doesn't really affect your rights: You still own the program, you may still use the program, and you may even still sue the software vendor if the program doesn't work as expected.

What the disclaimer is supposed to achieve is state that there was no contractual obligation to deliver a piece of working software. For software distributed free of charge, this might be viable, but I would find it rather surprising if such an obligation wasn't automatically implied to at least some degree by any commercial sale.

But this is above my pay grade as I'm not a legal professional or even amateur, for that matter.

That's a question that has to be answered by lawyers and judges. Personally, I doubt that blanket disclaimers really do much of anything in my jurisdiction.