This seems to come up a lot. A leader is not one who leads. A healing surge doesn't necessarily involve actual healing. And an encounter power has nothing to do with the nebulously defined "encounter"; it's just another recharge time. Apparently, just reading these terms and using their common language meanings misrepresents the ideas behind them.
It's jargon. Every game has it. And jargon works by redefining the "common language" meaning.
Leader very well could lead, and tend to have mechanics thematically conducive to that role. They are not obliged to, of course.
Healing Surge involves healing, in the jargon sense of the word of "increasing HP", analogous of the jargon sense of the word damage for "decreasing HP"
Encounter powers are generally usable once per encounter, with the assumption of at least 5 minutes of rest between encounters. The usability of Encounter powers is in fact directly tied to the game definition of "Encounter".
And to show that jargon is nothing new to DnD, let's look at some past jargon:
Armor Class: includes many factors other than armor
Touch Armor Class: in fact, specifically does
not include armor
Damage: simply loss of HP; due to the abstract nature of HP, does not necessarily mean actual physical damage.
Hit Points: often are not lost due to "hits"; most spells prior to 4E did not "hit". And really, trying to make sense of the phrase on the basis of pure common language is impossible; it makes no sense.
Hit: means "landing a solid enough blow to get past armor"; the common language definition would include any contact with the person or their armor, and would be better modeled by attacks vs Touch AC, instead of vs. AC. So Plate would not help avoid getting hit.
X per day: doesn't actually mean X times per day. It means X times, until reset by a full rest. Don't rest? Doesn't count as a new day. Oh look, that's almost identical to Encounter abilities in 4E, just with a different rest duration.
So, in short, the only difference with 4E's jargon? It's new.
In any case, that isn't the issue. Having two recharge times, with no interaction between the two, and tracking them separately for each ability is a problem in terms of both bookkeeping and explaining to your players why these limitations exist, even more so than the (again, hackneyed but established) Vancian rules.
Comparing high-level bookkeeping in 4E vs 3.5 is no contest. 4 Encounters/4 Dailies vs dozens of Vancian spells? I find it hard to believe that having two different types of rest is that complicated.
And why are explanations so hard? Since this is a thread about casting, set aside the issues with Martial classes. How is a spell that comes back after a 5 minute rest so much harder to understand than a spell that comes back after a 6 hour rest? Why is it so hard to understand how magic could work that way, and have different spells that require different amounts of rest and preparation? Is that really so different from spells with different casting times?