Another reason to not care about efficiency is prioritizing "pistonic" action of the driver, meaning the driver cone doesn't bend in-use. This is probably why YG speakers need big amps.
There are a lot of speaker designers who feel vintage woofers and paper cone drivers sound bad vs alternatives that may have much stiffer cones but lower efficiency. You can get some efficiency back with big and expensive motor design, but you're not getting 100 dB woofers with "pistonic" cones, just not happening! There is another way to have light coned woofers and reduce distortion though, you simply limit excursion by using more drivers, which also increases efficiency, but now you're looking at a larger speaker.
IMO speaker design without having an amplifier in mind makes no sense. For example, bass with high sensitivity mid and highs... you need to either design the bass section to be extremely efficient so the speaker can be powered by the same amp as the mids/highs or design the speaker for bi-amping. Yes, there are examples of speaker designers padding down the mids and highs over 20 dB (!!!) to meet the woofers but I think this is a bad idea!
In my speaker I chose bi-amping with a woofer that has a very stiff paper cone and a massive motor with a lot of excursion. It ends up being 94 dB, and it has very, very low distortion. For example my Pioneer S-1EX have the TAD 7" carbon fiber woofers, 2 per side just like the TAD Evolution tower speakers, but they sound quite warm and distorted vs my 15" woofer. I also chose a higher excursion model as a compromise because I only want to use one woofer. It requires a 5 cuft box to achieve it's low frequency extension and that's as big a most folks are going to want their speaker to be. Add a 2nd woofer and a horn? Now it's massive and nobody is going to buy it (relatively).
Sooo... imo if you want a very high sensitivity woofer section with low distortion and low frequency extension... if you want all that it's simply going to be large and expensive. No way around it. But today's woofers are AMAZING. At least some of them.
IMO you can find a good compromise in a modern woofer driven with a massive class-D amp. It gets a bad rap because of all the poor designs, but it's not the design, it's the implementation. It definitely CAN work, and it can work extremely well.