Here's a simple question about OD&D / AD&D / B/XD&D / RC D&D. (I imagine the question would apply to more recent versions of the game too; it isn't really a system specfic topic).
Nagol's analysis is probably close when looking at by-the-book xp for 2E and earlier, but the problem is that so few people actually did handle everything BTB. Not everyone gave XP for treasure. Not everyone required the high, listed payments for level training (or required level training at all). Some kept strict requirements to qualify for classes meaning rarer appearance of classes like paladins and rangers thus skewing perceptions. Most also ignored or freely extended or altered demi-human level limits also heavily skewing perceptions. Some just tallied xp for monsters and gold and split it equally. Some 2E games used optionaly individual awards schemes where xp was awarded for use of "class" abilities - spellcasters got xp for casting spells, thieves for the gold they actually stole, etc.
The AD&D system is also very resistant to analysis simply because there are so many variables. Thieves required less xp in general so they leveled up faster than other classes in general and typically would have been a full level or more ahead of others in the same party. The xp progression for any given pc to level up at any given level is HIGHLY inconsistent. Some classes are even and regular (if a logarithmic scale can be described that way) but take odd jumps where levels may suddenly require more xp or less than they otherwise would.
Adventure design was also not such that awards were likely to be consistent. In 3E as has been pointed out the whole xp system was well calculated to produce a constant, even rate of advancement for everyone at least as far as the NUMBER of encounters was concerned. Only the increasing duration of conducting the combats should have slowed the pacing of advancement from one game session to the next. Earlier editions had no built-in expectations of party size and they could be a dozen or more PC's - with accompanying henchmen, hirelings and NPC's making up a small army. They could also be just the typical, basic four cleric, fighter, mage, and thief by themselves. Predictable degrees of challenge were utterly absent. The equipment possessed by the PC's could still be mundane, non-magical stuff at 6th level - or they could be walking around with +5 Holy Avengers and Staves of Power at 4th. The DM could "challenge" an 8th level party with a dozen Kobolds or a dozen huge, ancient dragons and only the outcome of the battle and the subsequent feedback from players to tell him if things were too easy or too hard and only previous experience to rely on to figure out where in between the extremes he should be given the PC's actually involved.
(2) What were the design intentions (did EGG and company imagine that each level would take equally long to attain?)
I think as long as they were having fun and levelling up took place at a rate acceptible to both DM and players they didn't give a hoot what the actual numbers were (and the chaotic, haphazard charts and lack of discernable mathematical formulae shows it). They weren't "designed" with an intent - they were thrown out into the mix and if it worked it worked. If it stank, well it was probably published anyway and left it up to you to decide what to do with it.
(3) What do YOU think it should be?
A much slower pace than 3E. No award for treasure gained - unless it had to be gained by some other means than defeating guarding monsters/NPC's in combat but then the award should be based on the difficutly of getting the loot - not its cash value. It also shouldn't ALL be coming from just killing monsters. Story awards and achieving set goals should figure fairly prominently, not just the height of the pile of corpses around you. Characters SHOULD have different xp requirements at different levels but they should be reflective of what the character can do in comparison to other PC's. If wizards, for example, are deemed highly powerful at high levels then their xp requirements to reach those levels should have them advancing a LOT slower than anyone else to keep them in line. If a class is excessively weak by comparison he should advance RAPIDLY so he can catch up. Of course, there may also be reasons you WANT a character class to be weaker or more powerful at a given level, to advance slower or faster for reasons that have nothing to do with relative power of the class at that point.