As someone who worked on a major CDN I have some perspective.

> thousands of cold edges would call home simultaneously when all players players relogged at the same time.

Our more mature customers (esp console gaming) would enable early background downloads, spaced out over a few hours, the day/hours before 'launch'. Otherwise adhoc/jit is definitely best effort, though we did a few things to help:

Conceptually each CDN POP is ~3 logical layers 1) a client-request-terminating 'hot' cache distributed across all nodes in the POP 2) a shared POP cache segmented by content/resource ID 3) a shared origin-request-facing egress layer. Every layer would attempt to perform request coalescing, with 90% efficacy or more. eg, 10 client requests to the same layer 1 node _should_ only generate a single request to the segmented layer 2 cache. The same layer 2 node would we serving multiple requests to the layer 1 nodes, while making a single request back towards the origin.

Some exceptional behavior occurred, or was driven by, 'load' and trying to account for 1) head of line blocking 2) tail latencies etc from inequal load distribution. Based on load for an object, or a nodes current total load, we used forward signaling to distribute requests to peers. That is a 'busy' layer 2 node would signal to the layer 1 nodes to use additional/alternate peers. This increased the number of copies of a popular object in the segmented cache, increasing the total throughput available to populate the 'hot' L1 cache nodes _or_ to serve objects that were not consistently popular enough to stay in that distributed L1 cache. And relevant to your example we had similar problems when going back to the origin; In the first case we want to minimize the number of new TCP/TLS connections, which have a large RTT setup penalty, by reusing active & idle 'layer 3' connections to the origin. This, however, introduces hotspots and head of line blocking for those active origin connections. Which, again, based on 'load' would be forward signaled so that additional layer 3 nodes/processes would be used to fetch _additional_ origin content.

Normally this all means 1 origin request can serve a few orders of magnitude more concurrent client requests. For very large content, or exceedingly large client numbers, you'd see the CDN 'scale out' on concurrency in an effort to minimize blocking and maximize throughput in the system.

> One CDN vendor didn't even offer a tiered distribution system so every edge called home at the same time, another vendor did have a tiered distribution system designed to avoid this problem

See above on request coalescing. In the vast vast majority of cases it was effective in reducing the problem by a few orders of magnitude; AFAIK every CDN does/did that. _In addition_ we did have an distributed hierarchal system for caching between edge POPs and origins _but_ it was non-public/invite/managed by us for a long time. The reason being that the _vast_ majority of customers incurred additional latency (& cost to us) without meaningful benefit from this intermediate cache layer.

> The interesting thing was that no vendor we evaluated offered a robust preheating solution if they offered one at all.

This is interesting to me. AFAIK Akamai Netstorage was sold to solve the origin distribution angle, _and_ drove something like 50% of the revenue from large object distribution customers. For us the customer use case of 'prefetch' was perennial 'top 5' but never one that would drive revenue, and conflicted with other system tenets.

> One vendor even went so far as to say that they wouldn't allow it because it would let customers unfairly dominate the shared storage cache at the edge

That could have been us. And yes a huge problem is that you're fundamentally asking for control over a shared resource so that you can bias performance to _your content_ at the expense of _all other customers_. Even without intentional 'prefetch' control we had still had some customers with pseudo-degenerate access patterns that might consume 25-50% of the shared cache space in a POP. We did build shared quotas and such but (when I was there) we couldn't see a way to align the pricing & incentives to confidently expose that to customers. It also felt very very bad to tell a customer 'pay us $$$ to care about your bits' when that was our entire job, and what we were doing to the best extent possible already.

> we cap the connection counts to the back end and return 503s when we saturate.

Depending on the CDN you may be able to use `max-age` or `s-maxage` to implement psuedo backoff from the CDN. For us at least those 'negative hits' would be cached with a short (seconds by default) TTL to act a dampener in failure scenarios. Ensure that your client can handle/recover from the 503 as well, I'd expect the CDN to return those all the way through in the response.