Upon a serious note, I find backbone prevents, or at least somewhat minimises the amount of splaying that occurs once the hairs are wet, so a bit is required to prevent a mop.
I'd agree this is something 'backbone' would do - however it's got to be a very soft or poorly engineered brush that would have the type and density of fibres that would allow such extreme splaying to happen. You'd like to think that even the cheapest Chinese generic would test them out a tad to avoid this.
Seems to me in a
very generalised summation of lathering there's several stages to it involving the brush (assuming face lathering in this case as thats what i do 99% of the time).
1. Loading - putting soap onto the brush to convey to the face
2. Building lather - you might add water to the brush but you've got a lot of swirling etc, ideally the lather is building on your face but also inside the brush's knot
3. Spreading - you've got the desired lather consistancy, now rather than swirling you tend to 'paint' the lather around your face into the desired areas to the desired depth/thickness
4. Holding of lather + reapplication - generally subsequent passes might be able to be merely painted on using existing lather, other times you might have to 'rebuild/restore' the lather with a bit more of #2 type swirling - but the lather will build again a lot more rapidly than it did initially.
So if I look at where in those steps 'backbone' irrefutably assists to either building a better lather or the same quality of lather more quickly I am really unsure. In #1 I think natural fibred brushes with backbone do have an advantage over other naturals in loading quickly - I think synths negate this as they need less product to get the same ~result.
In #2 I think this is much of a muchness. Best practice user technique is different for a heavily backboned brush vs something much softer, so you'll find preferences either way. I do think a stiffer brush that provides more of a 'scrub' possibly gives a marginally more exfoliating effect than a softer one, I suspect the difference is far less than you'd expect from the brush firmness as the razor used after in both of them is the real remover of dead skin cells.
#3 I think lesser backboned brushes have big advantage in spreading and subsequent passes. Don't get me wrong I'm not talking about complete absence of backbone as
@Pjotr alluded - but the ability to have them splay/bend to spread the existing lather within them is much easier than say with a very stiff Omega 48.
#4 again I hope I'm not being biased but in theory and practice I'd feel less backbone brushes have the advantage here. I don't know about others but the really BEST lather is always that last big left right in the heart of the brush, that you often have to squeeze out. Lesser backboned brushes often seem to have more of this type of lather to give and release it much more easily. Once they've got a lather going too they are able to renew it a lot quicker than others.
You do also seem to find that in all the fibre types the ones that on a hair for hair basis have less backbone tend to be the higher priced/more desired fibres e.g silvertip badger>pure badger, horse tail>horse mane, Purtech type synth>nylon/syntex
Please don't get me wrong I'm not for a second saying there's anything wrong with people loving brushes with loads of backbone and all of us clearly enjoy having some degree of backbone in a brush. However, I do personally suspect it's one of those phrases thats bit misused to convey sentiments that aren't accurately depicted by the reference to backbone.
That's a very big topic, that needs a lot of thought...
For now: IMO you can achieve backbone just with the type of hair (boar, 2-band), density (chubby, epsilon), loft and shape of the knot (pointy bulb) - and of course a mixture of the above.
I also know, that backbone has nothing to do, if you can lather hard soaps or not. It's just different techniques...
I agree that QUALITY brushmakers will weigh the hair type/s, density, knot size, loft, and shape (which I think is a great and often overlooked one!) etc all up to make a great brush but I suspect the vast majority of the time they're made to a price point and significant compromise is made.
Agree 100% with your last point - IMHO thats one of the classic misconceptions about hard soaps & the brushes needed for them.