Sean's comments have been pretty much on the nose. I thought I'd add a couple more insights; I hope they're useful.
It's easy to forget that the game is an evolving entity, and that what seems obvious in 2005 wasn't so in 1998, 2000, or even 2002.
When PH, DMG, and MM were designed in 1998-1999, R&D simply didn't worry much about how one might honestly make aasimars, hobgoblins, drow, or ogres fully playable as PCs. They just designed all those monsters as best they could, translating their statistics from 2E to 3E in ways that seemed appropriate. The rules of of "LA" or "ECL" weren't really anywhere to be found (tho IIRC the DMG 3.0 had a vaguely playable kludge which at least allowed for the concept).
By the time 2000 rolled around, the FRCS team found themselves facing the difficulty of how to handle some of these "extra-powerful" races (particularly drow). As written, the drow were clearly better than regular PC races--not just as 1st-level characters, but at every single level. Even though the various abilities might not be as significant at 20th level as at 1st, the drow with 20 character levels is still mechanically superior to the elf with 20 character levels. That means that the player looking for mechanical advantages should always play a drow in preference to an elf, which runs counter to the assumptions of D&D and of the Forgotten Realms (Drizzt notwithstanding) and undermines the veracity (and verisimilitude) of the world.
In a perfect world, the aasimar, drow, svirfneblin, and other FR races would be of the same power level as the PH races, meaning that the choice between human and aasimar or drow and elf would be power-neutral (and thus entirely dependent on the player's preferences). But rewriting all those races for FR wasn't a realistic option (nor was rewriting the PH races to be of a similar power level as the extra-powerful races).
The solution that R&D arrived at was the concept of "level adjustment." Since a character's level was the clearest measurement of his overall power, adjusting that level was the clearest way for the extra-powerful races to "pay" for their benefits.
Is it a perfect solution? Of course not--it's a kludge, applied after the fact to handle a situation not anticipated by the original ruleset. (I don't mean this as a slam on either team--the 3E team's primary mission in designing, say, the hobgoblin was to design a good monster to fight rather than a PC to play, and the FR team was just doing the best they could with what they had to work with. All things considered, I think that both groups did the right thing.)
That solution was carried further through Savage Species, which examined most of the critters in the MM using the same tool. But remember that it's still just applying a kludge to monsters that weren't designed with it in mind. Is the hobgoblin a full level better than, say, an elf? Of course not--but with those juicy stat mods it's hard to argue that it isn't at least somewhat better mechanically. (And now we're back to Sean's point about "rounding up.")
By the time 3.5 rolled around, the decision was made to include LA information right in a monster's writeup (rather than forcing DMs to guess on their own). That makes it look like the monster and the LA were designed hand-in-hand, but for any monster designed before 2003 or so that just isn't true.
Fast forward to more recent design work, such as the goliath. I hear players complain that the goliath's way better than, say, the hobgoblin, even though their LA is the same. To that I say "you're absolutely right." Unlike the hobgoblin, the goliath was designed from the ground up to be a playable PC race. Thus, it represents the "cutting edge" of what a +1 level adjustment might look like. When doing what goliaths do best (using big weapons to smash monsters), the goliath is absolutely worth its +1 LA at the vast majority of levels (yes, it's a little fragile at ECL 2, but that goes away pretty fast). Sure, it feels a little inferior when it's doing something it's not designed for (like throwing fireballs), but that's like complaining that Domino's Pizza doesn't serve a good steak--it's not the point of the race. (And don't let anyone tell you a goliath can't be a spellcaster--I've seen goliath clerics, druids, and favored souls kick tall ass, as long as they focused on melee combat.)
More recently, though, you've seen fewer and fewer LA +1 races designed for PC play showing up in our books. That's intentional. The cost of a level adjustment, even when it's fairly applied, is perceived by many (maybe most?) players as simply too great a cost to pay for the cool features such races often get. The warforged, raptoran, and illumians all appeared as LA +1 races at various points in design or development. In each case, we aimed to bring them in at LA +0 to address this concern and to allow people to play them as starting characters. There's no doubt that some of these "push the boundary" a bit--certainly, the low-level warforged is a pretty tough customer--but overall we're pretty comfortable with the end results in each of these cases (and much happier than if they were more powerful and LA +1).
Looking back from today, if R&D could go back in time we'd likely make all the races in the PH a bit better. We'd give out some mental stat adjustments (such as, say, +2 Int to elves to back up the "elves are preeminent wizards" claim that gets passed around like candy--who does PR for these guys, anyway?) and a few more minor special powers (resistances, natural armor, weak spell-likes, etc.). That would, in turn, allow the "LA +0.5" races such as hobgoblins, aasimars, tieflings, and the like to become LA +0 "power-neutral" options for players to select.
We'd also probably kick a bit of power out from under the drow, svirfneblin, githzerai (+6 Dex? Bah), and other races that we'd like to see get played as PCs at least occasionally. Again, if these guys were "power-neutral" options people would choose to play them because they find them cool, not because they're uber-powerful.
And if we were really feeling rambunctious, we might even pick out a few "monsters" from the MM and make sure they were playable as PCs of a level equal to their HD (bugbear, ogre, minotaur, I'm looking in your direction...). If the bugbear had his current stats and 4 HD instead of 3, for instance, might he be playable "as written" as a 4th-level PC? Very possibly.
Anyway, there you go. Hope that's somewhat informative.