You're wrong. The whole point is this: in EU, you cannot chlorinate your chickens. This means that to sell chicken, you need to make sure that your chicken is good to eat without chlorination (by making sure your whole production chain is sanitized up to sufficient level).
In the US you don't need to make sure your production chain is super high sanitation quality because you can chlorinate the chicken afterwards. This means that you don't have to spend money/effort cleaning up your chains, because you can dip them in chlorine after.
From a health perspective there is honestly not that big of a difference. The resulting product in both cases is chicken that's safe to eat.
The real reason for the difference in policy is the incentives that it creates for the meat-producers. In the US there is no incentive to keep sanitation up in the production chains because the chicken will be chlorinated anyway. This actually incentivizes sloppy (cheaper) production methods over ones that are more sanitized but more costly.
On the other hand, in the EU you cannot wash chicken meat, so it needs to be kept clean and sanitized throughout the production process.