I think a "web app" should definitely be able to have some sort of more properly integrated filesystem API, but a "web page" has no business having access to such a thing. There just hasn't been a line drawn in the sand between the two, so every "web page" has all the capabilities of a "web app" by default.
Personally I wish there would be a meaningful line drawn between the two so that users could have a nice shorthand for allowing web pages to "upgrade" into apps which have access to things like WebGL and filesystem access. Such a thing would only have any meaning to power users and privacy oriented people though, and the general trend in browser design has been to spurn such users in favor of reducing friction for everyone else at all costs.
Personally I wish there would be a meaningful line drawn between the two so that users could have a nice shorthand for allowing web pages to "upgrade" into apps which have access to things like WebGL and filesystem access. Such a thing would only have any meaning to power users and privacy oriented people though, and the general trend in browser design has been to spurn such users in favor of reducing friction for everyone else at all costs.