Honestly where they are carried is almost secondary to the fact that we should get fucking scabbards/laces.
And yeah, of course the big ones aren't going to the hip....
Scabbards were often more expensive than the sword they contained: protecting the blade at the same time as making it readily accessible is quite an art. And talking of which, they look fancy too. In a way I think it's quite odd that Albion swords (being pretty much the gold standard for collectors of "replica" swords) don't come with them at all, but I guess the scabbard is the personalised bit. Fortunately a very good scabbard-maker lives nearby so my swords have some fancy clothes. And their blades have some protection from my sneezing.