Oh they dont ignore sound quality, as you say they are about clean output. My point is they have a preference of max spl over designed sound quality taste. One problem for me is that they are just too clean, and focused on being too low. This tends to lead to a lack of upper bass sound in the material they produce, hence the lack of character, because that is derived from the bass you can hear.
Low clean output is perfectly achievable from even a sealed design, it just costs more money, but you get what you pay for IMHO. Ive yet to hear any ported designed sound as good to my ears as a high performance sealed. You can argue all day that a ported design gives more output per watt/driver, and thats not disputable, but there is more to bass that simply getting the most spl from your driver. Sure you will get a linear response and sure your LLT will go very low, but from only having say a single driver, its at the cost of upper bass punch (unless you get this from your speakers, in which case an LLT is probably the more suited design) similar to a sealed sub with an incredibly low Q sound.
IB's suffered from this at first, before specific IB drivers existed. When you put a driver in a massively oversized cabinet, you rob it of its character and punch. IB drivers have a specifically designed response to counter this.
LLTs are good at what they do, but you just need to ensure that what they do is exactly what your looking for. For me, its not, they represent a cost cutting short cut to more spl at the expense of some of the stuff I like, and to be honest, wont be without.
Personally, if I was going to build say a couple 350 litre subs, rather than put in a 15" driver and tune to 15hz, I would rather use say a 21" driver (smaller cab comparatively), and you will get the same performance, but with a different sound character, but again it costs more money.