IMO it matters hugely. I made high tech self driving prototype cars in Italy along with a list of other Silicon Valley startups for a reason. They know their stuff up down and sideways. I've also been putting a lot of products in production in China for the last 20 years.
I'll give you some anecdotal evidence and you decide.
China - By law, every Chinese new year, all labor contracts are ended and new ones start again. Around 75% of the employees at your typical factory do not return and a fresh set of country bumpkins who've typically never even seen a coffee machine go to work. You can see people basically killing themselves in dangerous environments daily. I was reviewing my product line once at a factory where Lenovo was also painting it's laptop cases. There was a paint booth with foot thick doors and submarine window because the stuff they paint them with is that toxic. I look in the window at the robot arm painting laptops and THERE'S A GUY IN THERE WITH NOTHING BUT A DUST MASK LOADING THE SHELVES. I look at the manager and I say, how often do you change that guy? He says, "about every 2 weeks." They sit squarely between, "fking clueless & give ZERO fuks." Apple has its iPhones made at Foxconn the most expensive factory (over 800,000 employees) arguing that 'if X-quality, we'll be #1 in the world and we all make money + sub-X quality we're not paying for.' So they get X amount of quality. Everyone else, good luck. I've never once put something in production in China without flying there teaching, begging, negotiating, screaming, threatening, to maintain a minimum quality. They'll switch out your steel for pot-metal because they save $.003 on parts. And then you have to figure out why you've got a shipment of 10,000 parts that are breaking all of the sudden. It's a non-stop battle for bare minimum.
Italy
We made high tech car prototypes in Marenello, (near Ferrari, not far from Ducati) along with a lot of other car and motorcycle companies including Ford, because there is so much history there. Those people have been doing it for generations. I don't go to Marenello to teach anyone anything, they teach me and they are the best in the world at it and people in the car industry know it. If you ask a German, you may hear, it's Bavaria - everyone is going to have their opinion.
But the answer is ya, it matters hugely.