Some years ago I worked for a company creating streaming platforms for media companies, aka the clunky shit you complain about:-) My experience the clunkyness comes primarily from two things.

1: Every customer wants their own twist. It is not enough to create an awesome video player app and reskin it, no they all want to be special.

2: Getting the last 5% takes twice as much work as the first 95%. Probably even more.

It's quite doable for 'normal' engineers to make a steaming platform. You need to get the video files out there on some CDN, you need some service for the DRM keys (which needs to scale, and handle the different access packages), and you probably want some history and profile stuff. Easy enough. But for the best experience you want every video to start playing in less than a second. That means getting those starting video segments as close as possible to the customer, it means optimizing that DRM key delivery, and optimizing the player so it just gets that video pushed to the screen ASAP.