Sure I could get DNS to point to my ADSL connection and set something up in my router so that my home computer can answer the webhook but then I can never turn my computer off. On top of that I have about one power outage a month.
It would also be non-proprietary to spend $5k on a server and $300 a month on colo costs but with AWS I can use what would be 1 cent of resources if I was optimizing that colo (with $10k of labor) and pay 10 cents for it (could really be spending up to $50 on a non-optimized colo, which is what I might have if I don't need to handle a billion webhooks a month) If I want to switch to Azure or some other service that could answer a webhook the labor involved is minuscule.