There are many formulas for conventional fixers. Most are fairly simple and straightforward, and the variations are mainly due to different functions. Hardening versus non-hardening is a primary difference. Acid versus non-acid is another. Hardening is a venerable process from the early days of photography.
Photosensitive coatings are notoriously soft and delicate, especially when wet during processing.
Modern day films and papers are much less prone to damage when wet. In fact, they need hardener much less, or not at all. I have never used a hardener in all my life. Careful working methods suffice to prevent damage to print surfaces. An interesting fact about hardeners is that they demand an acidic environment.