The guy's a church accompanist. he doesn't play any advanced repertoire. a perfectly reasonable pursuit in itself, but a shockingly unqualified position from which to start taking a preachy tone about the supposed myth of incremental speeding up. Anyone has the right to detail things from their own experience from a place of humility and with awareness of what they can and cannot do, but it's to the severe detriment of the forum when people with minimal qualification think they are in position to dismiss particular approaches outright, in fields where they have not the slightest experience of overcoming the demands.
Thanks for that, very interesting! Clearly this guy is way out of his depth, but I wouldn't have picked this up given the rather over-confident tone in his posts!
Anyway, getting back on topic, I really do believe from experience that slow practice is absolutely fundamental, particularly resisting the strong temptation to speed up in the sections which are not so problematic, the danger being that I then trip myself up when a tricky few bars (or pages!) come round. I have learned this the hard way! I am currently learning the Wanderer Fantasy by Schubert. Very slow practice is absolutely essential, as in many other challenging works. A piece I have performed many times is the Ballade no. 1 in G minor by Chopin. That final Presto con fuoco is virtually impossible without very gradually building up to the required tempo. Also, hands separately first, then together, then separately, together, separately, together etc until the required tempo is achieved, and with total accuracy and total fluency!
It is not so important what the precise fractions of the top speed are; 'slow' means slow enough to train the fingers, wrists, forearms, upper arms, indeed the whole body, in the moves required, so that they become a series of trained reflexes, at any speed, including top speed.
Also, another advantage of slow practice is to allow yourself to become completely accurate in the reading of the notation without occasional wrong notes creeping in (e.g. missing some accidentals which affect later notes at the same pitch in a given bar). In this sense I believe that slow practice is also about being meticulous, and it also aids the memorisation process. I always start memorising a piece immediately, rather than just waiting till I have it up to speed. Also, I have been doing some more research and asking around my circle of pianist friends and colleagues, and it is generally accepted that Rachmaninov did practise very slowly; and not just to learn a new piece, but also to relearn or consolidate performances of works already known. Rachmaninov was a particularly great interpreter of Chopin for example, as well as his own music. e.g. check out the famous recording of Rachmaninov playing Chopin's 2nd Piano Sonata in B flat minor Op.35. Lots of accidentals in that first movement for example, and all too easy for misreadings to creep in. That's where slow practice comes in! Its not just about gradually building up to the required speed in a physical sense.
If all this seems too 'school bookish' for some people, well it isn't, it is based on direct experience over many, many years.