I'm much, MUCH rather have a one book solution like the (bestest RPG book ever) classic D&D Rules Cyclopedia. It was possible back then to put generation, combat, spells, monsters, DM guide, mass combat, dominion rules, world maps and more into just over 300 pages.
How come now, with our supposedly "leaner, better, more consistent" d20 rules it isn't? Progress. I love it
Most reasons for preferring three books are straw men in my mind. Your mind, of course, might be different. That's cool. Difference is good.
1) The "I need all the books because I have them open at different pages" logic: So, buy multiple copies of the One Book. It'll cost the same price as buying the PHB/MM/DMG. Or, use post-it notes, whatever.
2) The "My players share the books around the table" logic: As above, buy more books. Let them buy their own and have all the rules on hand. It also means more than one player can look at the same rules section at the same time, unlike the current 3 book solution where if one player wants to check the wording of a Feat while another wants to look up a combat rule, they'll either need to wait, or pull out yet another copy of the PHB.
3) The "the players will see the monster stats!" logic: well duh. They're online in the SRD (mostly), more experienced players are likely to know the more common monsters anyhow and I don't really see if it's a big loss if they do; I've been known to require an INT roll to see if the character remembers the monster's weaknesses before handing over the MM. No biggie. Heck, the players are going to check before or after the game anyhow.
4) The "they'll know all the secrets!" logic: to my mind, the Rulebooks should contain no secrets. They should contain rules. That's why I'm not too fond of rulebooks with adventures or GM-only sections. When it comes to campaign settings, I much prefer a two book solution - one Player's Guide and a DM's Guide. That way, the (world-specific) secrets are safe in the hands of the DM.
5) The "It'll be too big to make" logic: The D&D Rules Cyclopedia is 304 pages. Character generation takes up 26 pages, magic another 30, combat 13, monsters 67 pages. That's 136 pages out of the 304, the rest being take up with DM stuff, mass combat, optional rules, etc. I'd say that is very, very possible to achieve with d20 D&D. Sure, some monsters and spells will need to be cut, but I don't think many people will cry if the Destrachan or Horrid Wilting don't make the grade. A lot of the spells are just power-ups to existing spells anyhow (like the multiple Cure Wounds spells). They could all be rolled into one, surely.
6) The "It won't sell/WOTC will make a loss" logic: I'd buy one. Heck, I'd buy three. One for me, one for the shelf, one for the table. Imagine being able to give the gift of D&D at Christmas with a single book instead of balking at the $90 cost. A single book D&D with ALL the elements needed to play would revive the hobby, methinks.
I'm sure that are advantages to D&D being three books minimum (tradition aside), but for my money, the disadvantages far outweigh.