Many of them have managed object storage services as well. OVH[1] and Linode[2], scaleway[3] have them, that should scale for most use cases and are S3 compatible APIs

Also Azure and Linode, Scaleway Backblaze and others are part of Cloudflare bandwidth alliance [4] so there shouldn't be egress fees between the two.

It is really only AWS which is a problem, you don't need this setup with any other provider.

[1] https://www.ovhcloud.com/en/public-cloud/object-storage/

[2] https://www.linode.com/products/object-storage/

[3] https://www.scaleway.com/en/object-storage/

[4] https://www.cloudflare.com/bandwidth-alliance/

You can use block storage for scalable disk size: https://www.linode.com/products/block-storage/

If your cache is much smaller than the data, it will be ineffective, unless you think everyone keeps downloading the same tiny subset of files. That last assumption works for web content (e.g. newest articles see more hits) but probably not for data.