Basically, all "primary directions" are by default *heavily incorrect*. If you make an assumption that 3 degrees error (moon's path on ecliptic during 6 hours after birth) is negligible, you expect the real error to be at least one magnitude greater, so to be at least 10-30 degrees or more. And indeed, as primary directions/progressions depend on definition of a house system, so if your house system isn't working perfectly all 360 degrees of wheel, directions can easily be 100 degrees off in the 90th year of person's life.
Due to calculation time constraints primary directions were always calculated by approximate method. For instance, Leo's "Progressed horoscope" stated to neglect planet's own movement on ecliptic to simplifiy hand calculations (as the moon in 6 hours never moves more than 3 degrees, or sun 1/4 of degree). The math involved in any kind of calculations was time consuming enough to bother with it... Also Placidus was the only method employed and taught a century or two ago in England for this kind of directions. It was only because in other methods of house division to calculate primary directions precisely enough according to house system definition, you have to erect a new chart and then calculate planet house positions from it every few years apart. Otherwise the error of directed arc becomes too big.
The Ptolemy/Placidus method, because of it's house arcs parallel to equator, was at the time the only space-based house system method where primary directions could be calculated (ecliptic movements of planets neglected) with only one chart calculated, so with hand calculations in one day or faster. But Ptolemy/Placidus, as it is uncompromisingly based on astronomical theory that earth rest motionless in space and is flat, was already irreparably discredited more than half of millenium ago with the discovery of Copernican solar system theory. So it's no suprise that primary directions died out almost completely, regardless of the huge effort made by English astrologers in XIX and XX centuries.
New approach is to change studying the chart from "planet in house" into "planet in house's degree and minute", to increase resolution about 30 times (if you allow error on planet position to be +- 0,5 degree,) or 60 times if you allow error of +- 1/4 degree ( this exactitude is reached seldomly by rectification, but happens sometimes). This amplifies differences between house chart positions, for instance, two bodies with "3rd house" can change into 7th degree of the 3rd house, and 21st degree of the third house. It transforms "measurment" from element of "object in house" where are twelve houses, into degrees - 360 of them, where we can apply house aspect of planet to planet, and also apply transits to such positions, and hence get precision assiociated with dynamic and temporary nature of transits.
The advances in computer sciences enabled us to calculate any kind of primary directions/progressions list for any house system in a matter of seconds, not weeks, with computer program. Shortcuts and hand *approximate* methods are no longer needed. Nowadays we can calculate primary directions/progressions lists with body ecliptic motion taken into account, hence get most rigorously exact positions to the real movements of the planets on heaven. I use the term "primary directions" for hand crafted approximate calculations which neglect ecliptic motions of the planets, and "primary progressions" for algorithmically exact calculations, where ecliptic motions of the planets are automatically taken into account.
House systems are all time based
I don't call Placidus "time based" because every house system is based on primary motion of the earth (directly or, like Campanus, indirectly due to emplyment of east point of horizon and MC), and all of them are time based from this very basic assumption. Employment of small circles parallel to equator in house system construction it's not enough to justify calling it "time based" and deny this term to all the other house systems. In this respect even Regiomontanus is definitely more time based than Placidus is. And discovery of Copernican solar system theory actually make Placidus definitely less time based than quite a few other house systems. Employment of iterative part in the algorithm do not qualify it at all for justifying sticking this term "time based" to it, as this part of algorithm could easily be replaced by proper spherical figure solved analytically.
As to going to be born at equator (common argument), there is less distortion there than in higher latitudes, but it still exist - exactly at equator the arc between Asc and MC could be anything from 85 to 95 degrees. At about 30 degrees North (Alexandria) this arc could be from 75 to 105 degrees, at 52N15 (Warsaw, my location) it is from 54 to 126 degrees, and at 66 2/3 it reaches range from 0 to 360... as the day "as we know it" ceases to exist.