Should there be a free access to all museums worldwide?

Recently some German guests of mine expressed their surprise and delight that many museums of London are free. Being jaded, I answered that the permanent displays are free, but that you soon get bored of them as they seldom alter. However, the temporary (3-6 months) exhibitions are really expensive - up to £20 a ticket in some cases. But the parts that are free really are great and contain some stunning artworks and artefacts of historical interest, curated in interesting ways that capture the imagination. I certainly agree that national museums in other countries should contain free displays too. The Victoria and Albert Museum was founded in Victorian times on these very principles - good design should be available to view for free by anyone. In their case the idea was that craftspeople should have good design to inspire them, but I think that even if you are not an artisan, craftsperson or maker yourself it is always wonderful to see beautiful things, no matter what your income.