No source as in peer reviewed study, no, only anecdotal evidence (personal experience). To me, if you want less cars driving around, it would make sense to build the infrastructure in a way that they can get to their destination as quickly as possible.
And it is certainly not a secret that inner cities in Europe - apart from maybe the big tourist magnets - have been dying for a number of years. There's already a big threat for stores in cities through internet shopping, and I've heard of concepts to counter that by designing cities in a way that shopping trips will become more wholesome "experiences". That is, if you go for a shopping day, it's not just from one store to the next, but there's an offer of exhibitions, shows, music etc. mixed with excellent dining opportunities etc., all interwoven with the commercial stores.
But, if your "experience" begins with a drive designed to make it as hard as possible to get to where you want, I'm not sure it's going to work. You can try to change people's attitudes, but all things equal, for many people I would bet the ideal shopping experience would be the comfort of their own car to get to and from the shops, together with having the chance to drop off your bags every now and then in your own trunk.
I think you make a big mistake in framing this shift in city design to accommodate shopping. Its made to accommodate living. People need walkable safe cities to go to work, school, doctors, restaurants and yes, shopping occasionally.
The different is that this shift is not meant to improve a shopping street, is meant to improve a residential one that would have only parking and narrow sidewalks. If you walk in Amsterdam outside of the inner canal rings, you'll see people using the streets as extensions of their living spaces, little gardens, benches for when the sun is hitting just right, talking to friends and making birthday parties. The idea is to change the streets to be pleasant to be in, not just pass through.
With remote work and online shopping cities have to change from the place where we work, buy stuff and get the hell out to places we actually want to live in.
I've never claimed that this shift is being made (only) to accommodate shopping. But it's a fact that inner city shopping is in crisis and it is in the interest of city administrations to take counter-measures. However, the strategies to handle car traffic (probably, like you say, with the intention to improve other aspects of life in the city) are detrimental to that effort.
Not every potential customer of inner city shops actually lives in the city. As a matter of fact, where I currently live, none of the smaller suburbs and town in the vicinity of my next bigger cities do not have themselves alternatives for many of the commercial offers of the city. In other words, many many (potential) customers need to first travel to the city. If you ask these people, many will tell you that there is currently no viable alternative to the car for such a trip. And almost everyone would appreciate if their trip would be less painful, not more painful.
Of course you can argue that city planners should first and foremost care for the people that live in the city, not the ones that live around it.
So, if you think that the primary purpose of a city is to act as a sort of large shopping mall for people who live outside it, maybe I can _kind_ of see your point? That’s an exceedingly weird conception of a city, though, particularly given that, well, actual shopping malls have existed for some time. As has internet shopping. Like, if you’re trying to rescue the department store, you are way, way too late.
Though, also, even then, I’m not sure that you’re correct. The two main shopping streets in the city I live in are pedestrianised, and have been since the 1980s or so. There are a few (very expensive) multistory car parks dotted around the city, but, well, in practice you see plenty of people on trains and buses and trams with shopping bags from the shops on these streets. I think this is pretty much the case in any largeish city I’ve ever been in, actually; there’s generally not much parking on or near the major shopping streets.
