If that's the superficial cause, then the root cause is a lack of limits. Any production system in the world will go down from too much load if you don't limit the load. You have to do performance testing to determine what the system's peak utilization is, and put limits in place to prevent exceeding that limit.

There are multiple kinds of limits you need. First you need the raw i/o limits on things like networking, load balancer requests per second, etc so you don't slow to a crawl on high load; you can throttle max i/o so demanding users don't steal performance for others, or even throttle network traffic to the client IP and internal services. Then you need additional limits at app layer, like number of requests you can process that make DB calls (as most DBs have a connection and request limit), or limit API requests to X/minute. Then you need more business logic limits, like max number of concurrent logged-in users, max number of repos a user can have, max number of requests for free users, priority for paid requests, etc.

When you hit a limit, you have a couple choices. You can shed load (dropping calls immediately, which results in 503 errors for users, or even network disconnects), but it makes a very poor user experience, and can cause larger issues/conflicts in a distributed system. You can instead keep a max number of active sessions, and adjust that number over time, to ensure that (on average) your users have a stable experience; this requires implementing a "waiting room" for new sessions when old ones expire or log out; still not great for users, but it prevents everyone from getting random errors, which means the majority of users have a good experience.

There are way more kinds of limits to implement. Each business has to analyze its entire system to identify performance bottlenecks and implement limits to ensure the majority of users continue to have good service. Without those limits, you get a shit experience for everyone, your brand is tarnished, and customers run for the hills.

Finally, the performance testing helps you plan how much infrastructure you need to serve a given number of users. If you plan properly, you know X infra allows for Y number of users. Once you exceed Y users, you need to start throttling or stopping new user signup (and requests per minute) until you can increase capacity. Continuing to allow signups and additional usage, without the capacity to support it, results in what we see today.

But competent engineers know all this. If they had competent engineers, and it gets this bad anyway, the problem is management. Microsoft likely already made back what they acquired GitHub for. They probably figured they could keep riding the gravy train until the train went off the rails, and either eventually sell GitHub or write it off. Such is business.