Practicality

Slow changes and authority say-so. An example would be the Japanese system:

• Kanji system was copied from China.
• Hiragana is created by aristocrat women to communicate with each other. The system evolves with small changes. There were many variants of a syllable, until authority say-so that there shall be only one.
• Katakana was created by men and used in official documents, somewhat an authority say-so.

The all this mess has been cleaned to the modern format by multiple authority say-so, often ratifying the most common practice at the time. That bold part is really important because the change often goes to multiple directions and the authority say-so is a way to keep it together.

It would be really hard for English to become vertical because the letters have evolved to such that they are best red horizontally. The verticality of Chinese is because the ink and sleeves are not compatible.

Practicality

Slow changes and authority say-so. An example would be the Japanese system:

• Kanji system was copied from China.
• Hiragana was created by aristocrat women to communicate with each other. The system evolved with small changes. There were many variants of a syllable, until authority say-so that there shall be only one.
• Katakana was created by men and used in official documents, somewhat an authority say-so.

All this mess has been cleaned to the modern format by multiple authority say-so, often ratifying the most common practice at the time. That bold part is really important because the change often goes to multiple directions and the authority say-so is a way to keep it together.

It would be really hard for English to become vertical because the letters have evolved to such that they are best red horizontally. The verticality of Chinese is because the ink and sleeves are not compatible.

The idea for a real-life case:

The change would probably be in a language or an adoption of a completely new writing system. Horizontality is wide-spread and the current technology creates a lock-in for it. The best realistic reason I can invent for the change to occur is that machines get their own writing system. Not all robots have a printing machine, so the system is to be such that it is easy and fast for them. The change would probably be also in the language. People would then adopt this system by using the both systems in parallel, but slowly use less and less the old system, so that at some point the new system has replaced the old one.