I agree, monsters are not yet on the same ground as PCs (which is an assumption in the 3e system). One of the concepts I liked in 4e (which was not fallowed through) was the use of Racal advancement as an option by PCs. The idea behind this plays well for the 3.x monsters which are a combination of Class (monster type) and 'base' Race. Unlike PCs, monsters tend to advance their racial powers over learned class-abilities. Only this isn't actually how 3.x monsters are laid out.
CR is certainly a better place to start, which would also suggest dropping the idea that HD = Level. Level should equal Level, and everything else should be a 'benefit' of a class' level.
As for being Backwards compatible at this point the main consideration is keeping the monster playable as they are stated. That's the major trick.
Monsters as Classes/Races is a new system in D&D as of 3e, and hasn't been working quite right since the edition started. Not surprising since it's such a relatively new system.
I agree with the premise that HD+LA =/= Character Level. It is true that a mind flayer, or a rakshasa PC, under normal LA rules, get the great white shaft.
However, I do contend to OPs concept that CR = Character Level. Besides the obvious inconsitencies when a creature has a higher HD than its CR (most of them do), the real error lies in the following: Lifespan.
A "monster", that is, an enemy of the PCs, has at worst a lifespan of 1 round, occasionally 10 to 15, but with an average of about 5-6 rounds. A monster with a set of natural attacks, an alternate movement mode (flight, burrow, etc), and a special attack (breath weapon), gets to display those abilities probably about once or twice in a given encounter, due to usefulness (movement modes are often terrain dependant or counter productive to attacking), recharge (breath weapons and the like) or daily use limitations.
A "character" gets to use his abilities over and over, and recharge abilities like breath weapons are often always recharged when a fight starts. The hound archon is a good example: a relatively minor ability they have is the spell like ability "aid" at will. This means a hound archon, with his 6 minute duration via caster level and only a small amount of effort, provide for everyone in the party, including himself, an extra 1d8+6 (average 10) temporary hp and +1 to attack going in to every fight.
A big thing that would fix many monster as PC problems would be to make monster special ability DCs function as 1/2 HD + ability mod rather than 1/2 racial HD + ability mod. That way the abilities that are sucking up your levels via level adjustment stay useful. Nothing like the half-dragon sorceror who's breath weapon is a paltry DC 11 because he only has a con of 12 and no racial HD.
CR can't be the equivalent of character level - it's the marker of what's a reasonable challenge for four characters of that level.
If a CR 2 ogre was equal to a level 2 character, then logically one ogre is a reasonable challenge for four ogres. Which it isn't.
However, I do contend to OPs concept that CR = Character Level. Besides the obvious inconsitencies when a creature has a higher HD than its CR (most of them do), the real error lies in the following: Lifespan.
CR = Level is a good place to start, not the be all and end all solution.
Lifespan should also be considered for 'Monsters' which are actually class NPCs. Their CR is equal to their level and die just as quickly as the monsters if not more so. NPC wizards have no reason to hold back on spell casting and will fire everything they have every round until they die. An Ogre is supposed to be just as dangerous as an Elite Array Level 3 Orc Barbarian....
The HD error is why I, and others, have suggested removing the HD = Level. Hit Dice should be a class ability benefit that can be taken as options for a Monster (or even a PC class possibly). The major difference is that HD alone should not control things like BAB and Saves.
I am still working on my own proposal that is supposed to work with existing monsters and doesn't require any (or minimal) changes. The idea would be that a level of Animal would give the option of adding up to 3 HD plus bonuses to saves and attack, just HD/HP, some Race related ability (scent, pounce, etc.), or a combination there of.
I agree that many of the LA+RHD calculations are borked, but LA=CR is flat-out wrong.
First of all, CR was, in original concept, that an encounter between a party of four and an equal CR'd creature would result in about a 20% loss of resources (including HP, spells, arrows, etc.). So, if you have 1 Ogre facing 4 ogres, that 1 ogre should, in theory, be able to severely cripple one of the 4 ogres before going down (taking all but about 5% of the wounded ogre's HP).
However, CR doesn't neatly translate into LA because some things are very useful in a brief encounter, but game-breaking in a campaign. Use, for example, the Jann. It has a CR of 4, meaning I can play my 1st level Janni rogue in a campaign with 5th level characters. Of course, I'll have 6 Outsider HD in addition to my 1 rogue HD, I'll be able to Plane Shift my entire party at will, create food and water as a 7th level caster, Etheral Jaunt on my own, and turn invisible or fly around with impunity... and that doesn't include stat bonuses (which are a minimum of +2 to everything), telepathy, and hey, natural armor.
In a quick encounter, or an occasional NPC, those abilities are useful. They can feed a party, get them where you want them to be, and allow the NPC to avoid a fight (or sway it the way it "should" be). In a PC, that means the game is pretty much "The Janni and her sidekicks, the Colonels Nelson," unless everyone else is playing similar characters.
Really, in order to fix it, you have to make a more nuanced go at it. Outsider and Dragon HD really should count towards ELA; they're powerful and useful. Humanoid HD, however, stink on ice... I've taken to allowing people to replace them with levels of NPC classes, reflecting their role in the society they came from (I've also created a "Hedge Wizard" arcane counterpart to the Adept; uses the Witch list from the DMG, and the Adept rules otherwise). And, I think from that change we can gain a bit of insight; NPC classes count as one less for CR purposes; RHD for Abberations, Animals, Constructs, Elementals, Giants, Humanoids, Oozes, and Plants can be replaced with NPC classes (if the player so chooses) and are reduced in value for ELA calculations by 1.
This puts our Ogre at ELA 5; LA 2 + (RHD 4 - 1 because they're Giant and Giant HD are subpar).
It's not perfect, but it reduces the hit from playing monster races who were overvalued by WotC.