Nice to see results like that. I assumed clay would pick up the things that are normally broken down by iron remover and it did. So that proves that iron remover is not a must but if used before claying, it makes the claying process easier and with less chances of marring, as others said above.
On a bigger job, that involves a coating, I think iron remover doesn't add much to the cost and just gives peace of mind while making the claying job easier.
On a smaller job, just a wax or sealant after a polish job, then I think leaving the iron remover out is probably fine to keep costs low.
For a coated car that needs a decontamination job, then iron remover is the way to go IMO. I wouldn't clay a coated car if I don't plan on polishing it and applying the coating again.