Steering Box Ratio

the fast ratio pitman arms were designed for cars that were going to be used in specific race series. can't remember which but one presumes it involved going left most of the time.

Nope, totally wrong. The fast ratio pitman arms were designed for the TA and AAR cars. They raced on road courses, not ovals.

a sector based steering box is fast in the middle and slower towards the ends of travel. due to the way the pitman arm interacts with the cross link.
the twist of the sector is linear but the movement of the pitman arm stud in the cross link decreases the further away from central it gets (i.e 90*/ perpendicular to the cross link)

Nope. Someone needs to watch what happens to the center link when the pitman and idler move. I'll give you a hint, it doesn't just move linearly.

this is the opposite of what is built into modern steering which favours slower in the middle, and faster towards each lock. This cuts down no. of turns lock to lock. makes it easy to go straight, harder to veer wildly off course, or roll, if you jerk the wheel...

Nope. The steering ratio determines the lock to lock number of turns, that's true of rack and pinion and worm and ball and has nothing at all to do with the type of steering.

The self centering effect you're talking about is caster, which is higher on modern cars. But that has everything to do with modern tires, and can be adjusted on older cars with the right suspension components.

modern steering is slow in positions that favour going fast, and fast in positions that dictate going slower, like parking

Nope. Some modern cars change the amount of assist based on your speed or settings, but that doesn't change the steering ratio or how fast/slow the steering is. Changing the assist doesn't change the ratio.

if you extend the pitman arm. you make the system even faster in the middle. something you may not want..

if you never drive straight this is not a problem, its also faster either side of off centre, this is good for circle track racing. i.e the steering is now as fast off centre where you do most circle track driving , as it was in the centre as standard. It is now fast in a position that allows you to traverse a circle or oval race track. and very fast straight on where you spend little or no time when circle track racing.

a steering box that is too fast in the middle makes it much harder to go straight, and adds to a feeling of instability. you can offset this a bit by whacking in loads of positive castor and paying attention to toe in, but that is more expense.

if you have manual steering and you drive it on the street 90%
choose a ratio you want and use standard pitman arm

Literally none of this is accurate.

if power steering you already have 14.5:1 or thereabouts. and you don't feel the weight of it because its power steering...get a smaller steering wheel.

I mean, that's one way. But the better way would be to just reduce the amount of pressure produced by the steering pump, lowering the amount of assist. This has been covered lots with Mopar power steering because of its "over boosted" feel. Check out the article "pump it down". Small spacer change in the power steering pump, lower pressure output, heavier steering.

In my view
better to have manual 16:1 and standard pitman
than try to gain the same ratio with 20 or 24:1 and a long pitman arm
there will be cars and people who have balanced ratio and pitman arm length perfectly for what they want to do i'm sure....but for most of us easier to keep it simple

this is actually mostly true. But mostly because a longer pitman arm creates header and frame clearance issues, and if you can just buy a box with the right ratio and use a standard pitman the clearances all work. And standard pitmans and idlers are cheaper. Otherwise, final ratio is final ratio.

think about it from a leverage point of view

a sack of gravel:- That you can lift with 1 hand close to the body, would be impossible to lift with one hand 2 foot away with your arm out stretched.... leverage too much for you shoulder

Completely irrelevant example. The way your muscles work and the number and size of the muscles used by each lift have more of an effect on this than the actual leverage.

longer pitman you make it harder on the steering box internals and easier for the wheels to knock the steering wheel out of your grip
Basically easier to get busted fingers if you hit a hole or curb....
you need your hands to help you get out in a crash...

Ugh, no, again. If the final steering ratio is the same the force at the steering wheel is the same. Doesn't matter if the steering box is 16:1 with a standard pitman arm or if it's 20:1 with a fast ratio arm that makes the final ratio 16:1. Same ratio, same force at the steering wheel.