It's not a carry-over from their DVD business. It's a consequence of how they choose to stream. My assumption is that image-based subtitles are more compatible across a range of devices and clients, as you get to choose how they look beforehand.

You can definitely send subtitles as raw text and metadata – it's what they do on iOS devices IIRC, since you can change the subtitle appearance on the client.

Also, their ingest works with TTML (a text-based format): https://partnerhelp.netflixstudios.com/hc/en-us/articles/215... – this is a fairly widely used standard.