Folk traditions are notoriously fluid. There can be little by way of "set rules" on how to deal with the supernatural. In the same way, the same supernatural entities can be described in popular legend in contradictory ways.

Modern media has a way of "locking in" various species of the supernatural, codifying their behavior and other aspects of the tradition, creating dogma that the original folk believers would not understand or might find nonsensical. That said, media depictions of various supernatural beings are often based on something that was found in traditional folk belief. Historically, it is also true that written texts based on but deviating from folk belief can back feed into folklore, altering tradition because of the influential effect of the written word.

This is much of what has happened in the modern world: fairies/elves/etc. did not have insect wings (they flew without the aid of wings), but artists began depicting them with cute little wings; by the twentieth century many folk accounts of seeing fairies described them with wings, something inconceivable in folk tradition a century earlier.

The role of silver in discouraging the supernatural is a rare motif in European folk tradition, but thanks to media, it has become the pervasive "go-to" solution when attempting to defeat all sorts of supernatural manifestations. It is easy to imagine how this has occurred: the media creates a suspenseful storyline where people need to confront and defeat a supernatural menace; the protagonist must find the single, key ingredient to win the struggle; the protagonist obtains that thing (silver being a relatively rare but accessible previous metal mentioned occasionally in folk narratives); the supernatural being is thwarted. Silver, consequently, enters modern folk belief as the "traditional" way to defeat the supernatural even though that so-called tradition is grounded, largely, in the late twentieth century.

I'm not sure what you mean by "Is there a historical reason for these stereotypes" and "if these are based on history?" I've outlined the historical process by which silver rose in later modern folk tradition as an important means to defeat the supernatural. By your questions, however, it is possible that you are seeking some historical reason why silver should have been regarded as effective in this regard.

This hints at another modern folk belief: traditional legends from former times must be based on something in the real world. This modern folk belief is not always (perhaps we should said that it is rarely) based on anything in the real world. In addition, connections with the real world are largely speculative and cannot usually be proven. I have seen informal discussions about the importance of silver that point to the effectiveness of colloidal silver as a modern folk remedy for various conditions.

The modern line of reasoning goes as follows: silver is important in defeating supernatural opponents (even though this was not common in folk tradition); this must have been based on something in the real world (even though this assumption is based on a modern folk belief); colloidal silver is effective against various diseases (even though the effectiveness of this is disputed); this, therefore, is the reason why silver was regarded as effective against the supernatural (which is speculative, based on a misunderstanding of pre-modern folk tradition while imposing the modern folk belief that there must a "reason" for older folk legends). The beauty and power of folklore is that nothing that is written (here or elsewhere) can extinguish a folk tradition. The written word can affect folk belief, but folklore endures in the face of anything that is written.

edit: I see that while writing my post, someone else has provided a beautiful expression of the modern folk belief about why silver was supposedly regarded as effective against the supernatural. I suspect that the post may be deleted, so I provide it here in full:

Yes, there is a reason for this. Even when it is mainly not a historical reason.

Silver is slightly toxic to bacteria. It kills them. Historicial speaking, people did not know this, they only realised that it helped the people they treated with this „medicine“. With the decades went by, the people symbolised it a a pure metal and that it could help fight off evil spirits. The same goes for garlic.

I hope I could make myself understandable, because english is not my first language.

I am posting this here not to ridicule it: folk traditions are pervasive - we all have them, and modern folk beliefs are not to be ridiculed! I am adding this example because it is a perfect expression of just what I am suggesting is the modern line of thought with regard to silver. The connection of a trait of "slightly toxic to bacteria" to becoming the foundation of a pre-modern folk tradition of the defeat of supernatural opponents is speculative and grounded, in itself, on the idea that this was a common folk tradition (which it was not).