I'm thinking whether it makes sense in order to increase the speed of the website to do some strategy of caching the js files that are being included ?

one idea that I have is to do something like this:

[OutputCache(Location = OutputCacheLocation.Any, Duration = 3600)]
public JsController : Controller
public ActionResult JQuery()
{
//I would have a ascx with the entire jquery script inside
return View();
} 

and on the site.master:

<%=Html.RenderAction("JQuery","JsController");