Conceptually, I am not, but I do not like the way HS was actualized in 4e.
Begs the question, "shorter than what?"
If you have resource X, and you require 1X per encounter, in the case XY (where Y indicates the amount of X you have per game day), Y determines the number of encounters you can successfully engage in per game day.
But Y could be as low as 0 or as high as infinity. The actual value of Y would then determine what sort of encounter limitations were built into the system.
(And, obviously, the usage of X is an average, so there will be some variance as to how much Y corresponds to encounters/day.) Make it possible to replenish X faster, and you can eliminate the limitation (i.e., treasure that grants a healing surge, etc.).
RC
And thus, the more healing surges that you add to a character (or give a character access to, as you suggest), the more encounters that character can participate in. The 4e designers expected 4 encounters per day, but my group expects 6 - 12 encounters per day, so we use healing surges to meet that expectation (ways to replenish HS such as magical fonts, items and other features that provide surgeless healing, boons that grant the Durable feat, etc.).
In fact, if you also provide access to a bit of surgeless healing (but not quite as much as 3e had, because it didn't have the benefit of HS), my players can go as long as the situation or enviroment might need them to (but not forever).
If you want to have longer adventuring days but still have resource management (just like HP, daily spells, and Action Points provide), one good option is to add more healing surges to the game, not eliminate all of them or provide infinite, as suggested before.
This is one of the good ways that 4e started to eliminate 15-minute adventuring days. They took the vast number of daily resources (specifically with regards to spellcasters) and divided them into daily, encounter, and at-will. So instead of 6 spells per day, a wizard might of 2 spells per day, 2 spells per encounter, and 2 spells at-will (although the six spells likely share the same names as before, but are altered in power according to how often they can be cast, i.e. Magic Missile vs. Sleep). If someone wanted to go the rest of the way into eliminating the 15-min day, they might convert the remaining daily powers into at-will and encounter powers.
As far as healing surges go, I think they are basically 3e HP pools, but multiplied by 2 to 4 (depending on role). A party without surgeless healing (surgeless healing in fact, being all that was available to 3e characters, in the form of magical healing), might be able to do 1 or 2 fights in 3e, but would be able to do many more in 4e.
