Here's the problem: Throughout the publishing history of classic TSR-era D&D, no distinction was ever made in the player-type materials for different racial move rates. But, at the same time, in all of the monster-type materials there was a clear legacy of dwarves, et. al., having a slower move rate that other types. Which should take precedence?
Consider the following table compiled from early monster-book sources (including Chainmail, OD&D Vol-2, Swords & Spells, and the AD&D Monster Manual):
This chart shows a couple interesting things in the history of D&D monster entries. (A dash "-" indicates no value given, even if we could perhaps infer a value.) First and foremost, we see that all the move values present in Chainmail were simply transcribed verbatim into OD&D and then AD&D (excepting halflings); and so too all the armor values present in OD&D were copied directly into AD&D, regardless of any changes in rules for armor types (e.g., leather: AC7 or AC8?) or encumbrance. It's pretty obvious that the original intent was for elves to be in chain mail; dwarves in chain & shield; goblins and orcs in leather & shield. In fact, this matches up with the AD&D illustrations (as far as I can tell), although the AD&D text armor descriptions were changed to match the now-different meanings of the same numbers.
Secondly, it's clear that dwarves, goblins, etc., are always slower than such types as men or elves. More specifically, if we look closely at the armor types noted above and the official encumbrance rules, elves are faster than they should be (12" vs. 9" in chain?), dwarves and orcs are slower than they should be (6" vs 9" in chain; 9" vs. 12" in leather), and goblins are much slower than they should be (6" vs. 12" in leather?). Interestingly, however, halflings were actually made equally fast as elves all through Chainmail and Swords & Spells, until the AD&D MM came out.
To put it briefly, there's a clear tradition of dwarves (for example) being slower than elves -- in fact, basically half as fast throughout all these rulesets, even while wearing fundamentally the same armor type.
(Note that the AD&D DMG introduction of the "elven chain" type is pretty easily interpreted as a fix to the elves-apparently-moving-too-fast issue. Still, it does nothing for the dwarves-moving-more-slowly issue.)
While the general sensibility that "dwarves move slower, elves move faster" is consistently maintained all through the monster entries for Chainmail, OD&D, S&S, and AD&D, this is never reflected or addressed in the players' encumbrance-and-move rules. You can even dig up a quote from Gygax where he says, "I'd give the short-legged folk a base of 9" (at Dragonsfoot in 2005), but this was apparently never enough of a priority to actually put in any of the OD&D or AD&D player's handbooks. Not until 3E was there a version of D&D that codified slow-moving dwarf and halfling PCs.
So, again, which should take precedence? Personally, I'm torn. On the one hand, there's an argument for "more realism and detail" that the monster entries give us, arguing that short-stumpy dwarves really should move more slowly than other types. However, when I go to implement this in my own game I'm aggravated over certain players being hobbled, and having to explain to one player that their choice of race may slow down the entire party permanently. Even if everyone decides to strip armor for a surveillance mission (say), the party will remain slowed by any dwarves or halflings. Nor can I think of any fantasy story (Lord of the Rings, say) where a plot point was made of dwarves slowing down a travelling party or army.
Granted that such a rule never existed for PCs in any version of D&D (for the first 25 years), I'm prone to ignore it and have a somewhat cleaner system. In fact, the original game's (Chainmail through Swords & Spells) relatively fleet, speedy halflings give me something of a warm fuzzy feeling. But in any event, for things to be consistent, you've got to change either the movement rules or the monster entries in a way that was never officially done.