The problem isn't that 1954 definitions attempt to demonstrate that an oral tradition existed or to isolate the factors that made it what it was but its remit has been to foreshorten the natural consequences for traditional music. Instead of viewing that music as purely historical and the conditions which served its existence as no longer pertaining - which is a logical conclusion to make - traditionalists insist that the music can (indeed must) continue to be performed from a finite though broad set of material today. It seems like having your cake and eating it.
If the music limited itself to historical re-enactment (your 'museum') no-one could complain about folk as descriptive title. If on the other hand it presumes to occupy an oral space in the present it has to accept that the people transmitting it are creating a pastiche, they are infected by the whole range of musical influences - classical, pop, jazz and the inflections those forms bring. I'm much closer to your idea of folk as a museum but I fear that isn't the position many traditionalists will see of themselves, they will perceive their role as maintaining a living music. I can't buy that, the demands their modernity brings to it transforms the music.
If however the tradition saw itself as a springboard for contemporary folk (or whatever), a tradition that was wholly undiminished by what came subsequently and differed in subtle ways but was in keeping with sound and social space (a practical application I feel the vast majority of folk fans have embraced), rather than picking at the stitches of difference, logic would be served. Instead 1954 trads isolate the newer music as being no different to pop - fine, but lets not have any nonsense about living traditions, standard bearers and the rest of the bollox. The music is dead. This raises our circular and vexed question of wanting an authentic label because "then I know I'd like it", as though the tag was a guarantor of musical correctness.

In real terms folk exists in multiple spaces concurrently with people taking a relaxed view of nu-folk because its preoccupations, sound and performance resemble traditional music - singers may readily switch between the two in a set - and it offers the music the opportunity to find new audiences in the spirit of the tradition. Personally my listening is nearer 1954 but I trust my ears - a lot of the rest of the stuff I'm told is sung in folk clubs is not folk.