I run https://updown.io since 2012, a website monitoring service I created. I'm working about 5-10 hours per week on it. It makes about $6,000 per month and is still growing linearly. I also keep a full-time job alongside for now as an engineering manager. The key for me is to take time, make something useful, delight your clients, and don't try to become uber or airbnb.
I am a customer, I run a bunch of personal sites and hobby projects. updown.io is wonderfully cheap, the pay as you go model is perfect for my monitoring needs. I have no need for the stats, just the monitoring which it does well.
I'm curious too. Tracking your own website makes sense but there're definitely better ways if that's your own website. Why do people want to track other website regularly?
I think you're giving too much weight to what's in their example image. I use a competitor's free tier to monitor my own stuff. Using a SaaS is better for several reasons:
1. Don't have to install / maintain anything.
2. Who monitors the monitoring?
3. Monitoring from inside my network doesn't always fully approximate end-user availability.
That's pretty much it, my customers are people who have websites and want to be the first to know when there's an issue on it so they can fix it, in which case a SaaS solution is usually better than some internal tools because it eliminates setup/maintenance, keeps working when all your infrastructure is down and monitors everything (including internet link). Some other clients monitor website they do not own when they depend on it, for example as a vendor I could monitor Amazon if I sell products on it to be aware of any issue, or if I'm a digital customer engagement platform (what my full-time job does) I can monitor services I interact with like facebook API, twitter API, etc.
Probably half of the time (~2-3h per week) is spent answering questions/requests from clients or helping them diagnose downtime. I try to improve the product to make sure my clients don't need me so that when they do I can help them properly.