There are great sounding and not super expensive 2-way designs. Why go for 3-way, then?

My friend has been designing speakers, for HiFi, PA and MI LFSys. He is fastidious about the design of crossovers and does not use 3 way designs. He does use 10,12 and 15” woofers and compression driver/horns capable of going down below, the beaming region of the woofer. To get the correct response you must match/use the horn and comp driver, not necessarily from the same brand.

I use one of his designs, the Silverstone, an FRFR passive design that outclasses most HiFi speakers.
So he has a design philosophy, it doesn't mean he's correct. For a fullish range speaker, say 40Hz up, I can make very good argument for 3 or more way for hifi, bass guitar* or PA.

* My last large BG rig was 3 way, and was dismantled for my recent house move and is due to be rebuilt soon. It will also be 3 way and FRFR, but I've been using this sort of cab for over 20y. I pretty much only play 6s these days, B-C and E-F.
In honesty, I did a local party gig just before Christmas and used my old Peavey Mk IV/BW15 rig as it was to hand. It worked but was muddy. As the dance floor was full all night, I'm sure I'm the only one who noticed or cared.
 
https://www.audioholics.com/editorials/acoustic-research-ar9

The AR9 was a large floor-standing, vertical, 4-way, 4-ohm loudspeaker with two 12-inch acoustic-suspension woofers, an 8-inch acoustic-suspension lower-midrange speaker, a 1½-inch upper-midrange dome speaker and a ¾-inch dome tweeter.
The AR9 thus contributed to the science of sound reproduction and digital-measurement techniques, and this speaker design became a showcase for Teledyne Acoustic Research’s enormous investment in time and money during its development. The speaker was produced from 1978 to 1982 and sold well
 
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Well the "one" I know is a pair of sub plate-amps but limited to below ~200hz.

I didn't buy miniDSP because IMO the 2x4HD tried to do too much -- ADC and DAC couldn't be more than a few dollars in parts (quality). Even the (NLA) 2x10HD couldn't output 2-channel 2-way digital; would have at most served as EQ for main/fullrange driver digital (1-way, delay not supported) to external hifi DAC, using analogue outputs with delay for all other/lesser drivers.
 
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I love the sound of a 4" midrange driver. That's a reason why I like some 3 or more way setups. The midrange needs to be crossed no lower than 200Hz and go up to maybe 3500 kHz max. Works a charm for me, especially with a 3/4" dome tweeter.
 
Yes, you can notice the difference just by looking https://www.audiosciencereview.com/...urements-and-minidsp-2x4-hd-dsp-and-dac.2674/

1674808954724.png
 
Once you get the hang of op-amps and schematic + layout software, I can hardly see a problem with DIYing active filters. Yes, it can be tricky, but it can be damned good and satisfying.

NE5532x op-amps were always my go-to devices for audio. Cheap and hard to beat. A lot of supposedly better devices don't simulate as nicely, and only win the THD olympics on datasheets if they are run in class-b instead of a high bias. Since most filters rely on unity gain buffers anyway, I felt sorry for the op-amps, when I could sim 0.00x% or better thd with compound N+P pairs of SOT-23 sized mosfets.

It can be a case of "don't touch anything!" in case switching on the power amp and active filters in the wrong order creates a loud pop. But it's also an exercise in mental organisation to tidy up the loose ends in the system design.

I remember getting a 6ch Rotel amp years ago as a present for the family, and the first filters were passive and they sounded terrible compared to my later active boards. I passed it off as the passives being highly flawed, but over time I also came to understand that the amplifier also had a limited ability to cope with the phase-shifted loads. Exactly why a passive XO could compromise a class-ab amplifier's distortion is hard to explain, but the same reasoning also vindicates some design choices like class-a with little or no negative feedback, with passive XOs. Nevertheless (making it at least slightly related to 2-way vs 3-way), adding an extra way would still be best received if extra amplifier channels are also added.