IMO this is terrible advice.

1. Put a moderate amount of money toward having the world's experts in uptime keep your site performing fast, and accept that occasionally your service goes down at the same time as everyone else.

2. Roll your own service, hire a large number of expensive experts to try to solve these problems yourself, and be responsible for your own outages and failures which will happen eventually and probably more frequently.

If no one is going to die from your service going down, it seems like this is a perfectly reasonable third-party dependency. And if the issue is just your contract's SLA or a financial customer, the saving that comes from using Cloudflare can probably be worked through via negotiations.