Ubiquitous access is an increasingly common vision of computing, wherein users can interact with any computing device or service from anywhere, at any time. In the era of personal computing, users with visual impairments required special-purpose, assistive technologies, such as screen readers, to interact with computers. This paper investigates whether technologies like screen readers have kept pace with, or have created a barrier to, the trend toward ubiquitous access, with a specific focus on desktop computing as this is still the primary way computers are used in education and employment. Towards that, the paper presents a user study with 21 visually-impaired participants, specifically involving the switching of screen readers within and across different computing platforms, and the use of screen readers in remote access scenarios. Among the findings, the study shows that, even for remote desktop access - an early forerunner of true ubiquitous access - screen readers are too limited, if not unusable. The study also identifies several accessibility needs, such as uniformity of navigational experience across devices, and recommends potential solutions. In summary, assistive technologies have not made the jump into the era of ubiquitous access, and multiple, inconsistent screen readers create new practical problems for users with visual impairments. Copyright is held by the owner/author(s). Publication rights licensed to ACM.