Are there any edge function hosting services that focus on replacing centralized API processing with edge execution?

Yes — there are several edge-function / edge-runtime platforms that can be used to move API logic away from centralized servers and run it closer to users. If your goal is specifically to replace centralized API processing with edge execution, these are the most relevant kinds of services:

Common options

• Cloudflare Workers
  Probably the most well-known for this use case. You can run API logic at Cloudflare’s edge network, and it’s often used as a “global API layer” or to proxy/transform requests before they hit origin services.

• Fastly Compute@Edge
  Designed for low-latency code execution at the edge, including API request handling, auth, routing, and transformation.

• Akamai EdgeWorkers
  Similar idea: execute logic at the CDN edge for request/response processing and API augmentation.

• Vercel Edge Functions
  Useful if your app is already on Vercel and you want edge-located API endpoints, though it’s more app-platform-oriented than pure API infrastructure.

• Netlify Edge Functions
  Good for edge request handling, lightweight APIs, personalization, and middleware-style execution.

• Deno Deploy
  Runs JavaScript/TypeScript at the edge and can be used for global API endpoints.

More “infrastructure-building” oriented

• Fly.io
  Not strictly “edge functions” in the same model, but lets you run containers close to users in multiple regions, which can serve a similar purpose for API workloads.

• AWS Lambda@Edge / CloudFront Functions
  For AWS-centric setups, these let you execute logic at CloudFront edge locations, though the programming model is more constrained than some others.

If you mean “replacing centralized backend APIs entirely”

That usually isn’t a complete drop-in replacement, because:

• edge functions are often best for routing, auth, caching, personalization, transformation
• stateful or heavy workloads still often need a core backend, database, or service layer
• some platforms limit runtime, memory, networking, or database access

So the most common architecture is: edge API layer + centralized data/services, rather than fully eliminating centralized processing.

If you want, I can also give you:

1. a comparison table of these providers, or
2. recommendations based on whether you care most about latency, cost, developer experience, or compatibility.