I haven't a clue about dosage, but McKeown's brief article is aimed at a mainly US bias, and a bias based largely on what were old dirt tracks. The animals were developed to a conformational type to suit sprinting, in the same way that humans are developed to suit sprinting (and don't think genetics don't play a role!) - horses with gluteal mass and strong gaskins (thighs), but overall a smaller, denser animal. Think of human sprinters' big powerful bums, versus the human distance runner - entirely different frameworks and body build, for entirely different purposes.
The rangy animal he longs for probably started passing into history around the 1930s, built along the Barb horse heritage of Thoroughbreds, rather than the Arabian. If you look at Arabian racehorses, just expand them by an eighth and you have today's typical sprint type. The Barb was, and is, a North African strain which was interbred with the Arabian to kick off the Thoroughbred breed. They are taller, more angularly built, with a sharper - you might say pointier - outline, and a predisposition for endurance. The Arabian, more rounded and compact but equally very hardy and strong, but more able at speed.
It's the Barb strain's heritage which has been disappearing from Mr McKeown's longed-for 'good old days', since while it possessed great durability (living on into active life for a good three decades), it didn't possess the spike speed of the Arabian. Thus the Arabian type prevails today in sprinters' shapes.
However, the Barb strain does still live on, expanded and developed, in true jumps racehorses - DENMAN possesses the plain straight head, the angular outline and the slabbier look of the Barb. Barbs could grow to up to around 15.3, 16 hh, so improving feeding, hygiene and care over centuries has seen that height increase by up to a hand (four inches), the body shape nonetheless changing little. The ability to gallop relentlessly, but more slowly than the Arabian, is there, and that's the main difference - the rangy, angular type is your better NH horse because of his Barb heritage; the rounder, more compact type is your better Flat sprint horse because of his Arabian pedigree.
The 'need for speed', or perhaps the 'greed for speed' has grown out of the ability of the Arabian type to be ready earlier and to outspeed the rangier, Barb type. Thus, breeders developed a type, a shape, that took to winning more races. Any races. Over time, the USA in particular cast off the slower Barb type in favour of the Arabian type, which, also because of its overall lighter weight, favoured the hard impact of the American dirt tracks.
These tracks were very unforgiving on developing bones - and still are. To keep their horses going, trainers used proprietary anti-inflammation brands and that's why you see American horses being allowed to run on 'Bute' (it's got a helluva long butylthingywotsit name I can't think of!), which masks joint pain caused by impact stress.
Lasix (there's another endless latin moniker for this, too!) is an anti-bleed agent which is also approved for use in the States, and is used in training here, but has to be withdrawn by (I think - jinnyj?) 10 days before a race. American horses run almost traditionally on the stuff, given that all horses bleed a small amount under race stress, but not all show. The Americans prefer to keep bleeding minimal and use the drug routinely. Thus, you may well have US horses running on both drugs.
I stand to be shot down in flames on any of this, but it's my take on the US scene and the overall TB evolution to date.