According to the documentation of glDeleteFramebuffer, "if a framebuffer that is currently bound to one or more of the targets GL_DRAW_FRAMEBUFFER or GL_READ_FRAMEBUFFER is deleted, it is as though glBindFramebuffer had been executed with the corresponding target and framebuffer zero". Currently, the m_boundFBO is not reset to the default value, meaning that the next call to the bindFramebuffer will avoid to set the same framebuffer id. As soon as the old framebuffer is deleted, GL is allowed to reuse the same identifier for the newly created framebuffers.
WebGL Rendering Context code already has this covered.