I have to use subtitles for sensory issues and this [small subtitle] bs gives me migraines. Makes me give up on games!
pocketlin, via Twitter

Haven’t really found small text to be a problem to be honest. Overly large ones though, I find annoying. Would be nice to have some options so people can set it to something they prefer.
Puppetslave, via Neogaf

While ensuring subtitles/captions are presented in a readable way by default is a good first step, there are multiple use cases for them.

Some people have no access to audio, and are reliant on understanding every single word, so need them to be as clear and obvious as possible, with access to extra information such as who is currently speaking. Some others use subtitles for localisation, so still need them to be clear and obvious, but have no need for extra information. Others still only glance at the text occasionally, for example when an explosion goes off during an important moment of exposition, or when a word is missed due to it being spoken in a hard to understand foreign/alien/robotic accent.

In additional to these, there can be clashing requirements between the text needing to be as readable as possible, and needing to fit with the art direction of the game.

For all of these reasons, allowing player to configure how the subtitles/captions are presented is an effective and relatively easy to implement solution, and a solution that is standard in other industries too. For example Netflix and YouTube both have extensive caption customisation menus. Areas that could be made customisable include:

• Text size (including 46px@1080p)
• Letterboxing, ideally a sliding scale between on and off to allow control over opacity
• Font, e.g. easy read Vs art director’s choice
• Whether to include additional names and color-coding to differentiate speakers
• Whether to include closed captions
• Whether to include background conversations

Additionally, some major console and mobile platforms have the ability to configure some of these things at system level, and provide APIs for developers to query and pull in as their default values.

Best practice example: Life Is Strange
Best practice example: Rise of the Tomb Raider
Best practice example: Dragon Age: Inquisition
Best practice example: Hitman
Best practice example: Silence

More information: How to do subtitles well: basics and good practices
More information: Accessibility functionality available in the Xbox SDK (video)