The problem with two spaces following a period is that it looks like one could drive a truck between sentences.
The double space was developed with typewriters because they worked with monospaces – where each letter was given equal room – instead of the typesetter’s prortional spacing.
With the advent of typewriters a writer began to gain control of the typesetting of the text on the page. Poets after typewriters write with an eye for how their words look on the page, for example. Computers push this farther, with the writer allowed to consider fonts, sizes and even in some cases leading and kerning.
I was reading an interview with with Mathew Carter, the designer of Georgia and Verdana (two of the first high-quality typefaces specifically designed for screen resolutions. Carter is one of the very few typeface designers who is designing for the computer. He’s been called the most important designer of the 20th century and since he’s still working he could easily become the most important designer of the 21st as well.) and was amused to hear him say that when he started the business, he hated trying to explain what exactly he did. Today, due to the advent of computers, he says he can have perfectly intelligent conversations about fonts with 9 year olds.
Style develops with technology. This was true with the calligraphy of the monks, the typesetting of Will Caxton, the typewriter of Ezra Pound, and the single space after the period with today’s knights of the blinking cursors.