Your first seconds probably need to show the outcome, not the service. For a web agency, faceless can work if the video opens with a specific before/after or a problem a business owner recognizes: "your contact form is leaking leads", "this restaurant menu takes 6 taps to find", etc.
I'd build a simple repeatable format: 1) show a bad example for 2 seconds, 2) explain the cost in plain language, 3) show the cleaner version, 4) end with one takeaway. Screen recordings, site teardowns, Loom-style cursor videos, and simple captions can carry it without your face.
Also make the content for one buyer, not "everyone who needs a website." Pick a niche for 2 to 3 weeks, like dentists, local contractors, gyms, cafes. The more specific the examples are, the less boring the video feels.