We can import chicken now from the USA. We already have loads come in from Thailand.
But what the EU have in place are high tariff barriers on agricultural products which forces up the prices of imports from areas with no specific trade agreements.
So don't think this is about standards. It isn't. It's about maintaining a high price mainly to support the EU mainland producers in Southern Europe.
It's a strategic decision. A political decision.
Then, due to shortages, sometimes seasonal, the EU has made some deals where some countries have Tariff Rate Quotas.
So (for example) if chicken is 40% duty, a country like Thailand has a TRQ of say 500,000 tons that is allowed to come in tariff free.
That limits the total quantity that comes in from outside the EU, as once that TRQ is reached, no more can come in because the higher tariff kicks in and it isn't commercially viable.
So back to the Thailand chicken.
Typically Thai chicken is not reared to EU standards. It is the specific suppliers that supply the EU that specialise in rearing their chicken and so apply the EU standards to the production process. Importers will have full time QC in those facilities to check the animals are reared ethically, the staff are treated ethically and there will be also be a rigorous quality checking.
That could have happened in the USA had we any arrangements in place. The US producers do not have an arrangement to supply the EU, so they rear their chicken to the standards of the markets they supply. Had there been an arrangement to supply the EU I'm sure some US producers would have considered whether it was viable to produce to EU standards in their facilities and aim at the EU market.
A trade agreement with the US doesn't mean that the UK has to accept the US standards or vice-versa, although it may agree some aspects of mutual recognition in some sectors.