Is the ideal multi-way a 3-way with limited bass?

Perhaps, but it really comes down to acoustical design of the speaker and materials, and while I think 3 is somewhat ideal at this point, I would say for similar and different reasons.

I agree on the issue of doppler distortion, even though there are some good 2 ways with relative deep bass and high cutoff frequencies.

Smooth dispersion without resonances off-axis is critical in my mind, which also calls for limited bandwidth per speaker, though acoustical methods such as Paradigm uses for dispersion and materials like Magico uses allow good wider bandwidths per speaker than practical in the past.

And even if we talk about a woofer, should it be one big or two small? I lean towards multiple small as it keeps the dispersion closer at the crossover point.  I like to have that next crossover out of most of the vocal range if I can.

I may have found the perfect 3-way in Revel Gem2. Standing free in the room they produce nothing below 80-90 Hz. Which is perfect. With some dirac processing and three high-quality subs you have a fabulous full-range sound. 

How about Rega’s side firing bass driver? This seems to be a great implementation in a floor stander allowing flexibility and tuning to the room. 

Like the looks of those gosta. When things are normal again, may have to go find those. I have been looking for a good high end home theater speaker.

You are always trying to make smallish speakers more than they are.  :(