So.. I really don't know chemistry, and these aren't the highest quality references, but here goes:

• 4 mol of iron in a heat pack provides 1648.4 kJ of heat. ^[1]^
• 4 mol of iron weighs 223g. ^[2]^
• Recycling 1000kg of steel saves 642 kWh of energy. ^[3]^
  • Recycling 0.223kg steel saves 642 * 0.223 / 1000 = ~ 0.143 kWh
  • 0.143 * 3600 = 515 kJ

Huh. So maybe heat packs are a reasonable use of scrap iron's embodied energy after all. Assuming you have a sufficient source of uncontaminated steel filing waste and that it's economical to collect and process into heat packs.

...But only if you're heating your water using fossil fuels using an inefficient method! If your water is heated using solar or waste heat capture or a heat pump^[4]^, which would swing the balance way over to hot water bottles again.

1. https://brainly.com/question/16900421
2. https://www.convertunits.com/from/moles+Iron/to/grams
3. https://lbre.stanford.edu/pssistanford-recycling/frequently-asked-questions/frequently-asked-questions-benefits-recycling
4. https://www.eec.org.au/for-energy-users/technologies-2/heat-pumps