If we are the only ones imposing climate regulation, businesses and industries will move abroad where it's cheaper to operate

What are you even talking about exactly. EU regulations for what cars are allowed will be exactly the same whether the cars are manufactured in the EU or elsewhere. And carmakers already have different factories in different regions of the world to serve each market.

Honestly, without some strict rules for European and US car manufacturers to get their shit together, they're only going to fall ever further behind China, which has the biggest EV manufacturer already. Fossil fuel burning combustion engines don't have any future anyway, because fossil fuels are finite, the climate crisis is accelerating ever further and EV are getting more and more competitive (they're already cheaper in the long run for mid and higher class cars). Carmakers aren't being done any favours by allowing them to drag their feet and become ever more obsolete.