I have a pair of Thiel CS6 speakers which have first order crossovers plus a concentric mid/tweeter. This crossover design makes each driver cover a much broader frequency range. Theoretically this would worsen any doppler effect. Other Thiel models have the same characteristic - they use first order crossovers and several models have concentric drivers. Vandersteen is another example of using first order crossovers.
I’ve read dozens of Thiel speaker reviews over the years and I’ve never seen a reviewer mention anything about the doppler effect altering the sound. In fact I’ve probably read over a thousand speaker reviews in my life and I don’t recall anyone ever mentioning doppler. You would think that golden eared reviewers would race to tell you about how their exceptional hearing detected that they were hearing the doppler effects of a particular speaker.
I’m going to stick my neck out and say that the doppler effect for speakers isn’t a thing. I wouldn’t be surprised if some company cited this as a reason why their speakers are better but I suspect that not all marketing hype is real. Except when it comes to cables where you should believe everything the manufacturer says.