Is there any hope of getting my pictures back after an iPhone factory reset some day in the future?

Modern encryption is strong enough that there is no way to retrieve the lost data without the key. Although it's possible that it could be doable in the future in theory, consider that even the cipher 3DES, a trivial modification to a cipher designed nearly half a century ago in the 1970s, cannot be broken in the manner you want, and that was cryptography in its infancy. Modern iPhones use AES which has held up to 20 years of analysis and is showing no signs of meaningfully weakening.

Ciphers are never secure one day and fatally broken the next. There is virtually never a massive breakthrough that renders a cipher useless, as attacks are improved incrementally. If AES ever gets broken badly enough that you would be able to recover the encrypted data without the key, there would have been decades of slow improvements to the attack and we would all have known for years that it's too weak to even consider using. If that were the case now, I'd tell you to wait a few decades and maybe, just maybe, a key recovery attack would be released, but that's not the case.

The data is gone. Plan for keeping backups in the future to avoid a repeat of this issue.

Every time I updated my iPhone with iTunes, iTunes automatically made a backup of the iPhone. These backups can be checked in:

iTunes >> Edit Menu >> Preference >> Devices >> Device backups

(Some backups might even be automatically moved to the Recycle bin)

Isn't it possible to use one of these backups to restore to a (new) iPhone as described by Apple Support?

Modern smartphones encrypt data backed by Trusted Execution Environment (TEE). TEE stores keying material that is used together with master key and screen lock code to derive a key that encrypts and decrypts keys for device encryption. This is one possible way of protecting device encryption keys using TEE, Apple's implementation can be slightly different. On factory reset, TEE flushes master key and regenerates new key on first boot.

There are no scalable and affordable techniques to extract data out of TEE. If their Evaluation Assurance Level (EAL) is 4+, they can be as secure as smart card which is tamper resistant by design. If there would be such a forensic tool in future that could recover deleted keys from TEE, you might be able to decrypt recovered data if it's not already overwritten at present. You will be needing electron microscope for this.