I'm pretty sure that there exists no law forcing the holder of a
patent to allow others to use it.
There are no such laws. Though the government has in some cases forced the licensing of patents, e.g. some of the intergovernment deals on AIDS drugs, and earlier the Wright patents for military aviation in world war I.
And even if there was such a law, it's still the decision of the
patent holders, what price they demand. They can exclude everyone by adjusting the price. And there's no reason why they shouldn't define different prices depending on who wants to use the patent...
Differential pricing is tricky, any such scheme can easily run afoul of anti-trust laws. So the claim of "no reason" here is dubious.