To be fair, though, as 3e went on many pre-published adventures (and notably the Paizo adventure paths) tended to abandon the 'correct' pacing of encounters in favour of fewer, tougher encounters (indeed, I believe one of the Design & Development articles mention that this was the case - that the expectation of 13 encounters per level had shifted to be more like 10 or even 8).
My observation, too. The 4 encounters per day and 13 encounters per level assumption in the core roles tended to be abandoned if using these adventures.
Of course, if each encounter is tougher, each will use up more resource, and so the party will have to rest more often. Take this too far and you get the 15-minute adventuring day.
However, even with that I'm really not sure the 15-minute day is really that much of a problem. So the PCs only complete one encounter in the day, so what? It's not like the players around the table actually have to wait a day before they carry on, all it takes is for the players to say "the Wizard casts rope trick and we wait out the day", and for the DM to say, "okay, the next day, you proceed onwards..." and you're done. And, if that really bothers you, you could always just replace the 'replace expended spells with 8 hours rest' with 'replace expended spells after an hour's rest' and go from there. Since it's bound to be little more than a handwave most of the time, does it really matter which handwave you use?
The reason why this could become a "problem" as I see them:
o It are only Spellcasters that really can go "nova". Their powerful spells are what decides a high EL battle. If you have the habit of 15-minute adventuring days, spellcasters will seem overpowered, because the theoretical balance mechanism in careful strategic planning (operation play) became negated.
o Once you've had a few "nail-biter" high EL encounters, regular EL encounters become a little boring.
I think a major contributor here are the out-of-combat healing options, too. Normally, the primary daily resource a Fighter has to manage are his hit points, helped by Clerics or other healers. Cheap Wands of Cure Light Wounds change this - hit points are not really a daily resource, but an encounter resource, and so is the Clerics healing.
But an EL = PL encounter is supposed to cost around only 20-25 % resources - which essentially means that the Fighter, Rogue and Cleric can handle the fight (without the Cleric using much spells) and the Wizard can safely (from a resource management point of view) watch from the sidelines (Some Wizards might use Wands of Magic Missile, Crossbows to make an "alibi contribution", well knowing that this is not the fight they should waste something vital on).
But a combat where people don't throw a lot of spells around is a little... boring. After combat, the spells used will be from the Wand - Cure Light Wounds for all. (Heck, our group did stop rolling 1d8+1 and just assumed an average of 5 or 6 points healed per charge, and the Wand-users would ask how many charges they had to give up.)
At the end, the whole notion that the fight could cost 20 % resources was just wrong. A Wand of Cure Light Wounds is not 20 % of the parties resources beyond level 4+.
In addition, an EL=PL encounter also suffers from the fact that you fight either several weaker foes or one equally strong foe, and as such is often not that interesting. You hit easy, they miss often, or people can just "focus-fire" on one opponent.
I think the real "math" error in the system is the assumption that EL=PL would always cost parties 20-25 % of their resources. That's just not true thanks to the Wands. Wands remove the entire balance and pacing idea behind the 4 encounters per day on average concept.
The other error is not accounting for play dynamic and the "mindset of gamers" - which is a bit shizophrenic. Gamers will always look for the "safest" or most effecient way to play the game, and if 15 minutes of adventure per day is safe or efficient, they do it. But they also want a challenge, so the DM (or adventure writer) provides them with harder encounters, which makes the safest route not just optimal, but the only viable route.
From a adventure design or pacing point of view, this all leads to some limitations.
- Time Critical adventures are hard to make. Assuming optimum play (use of Wands of Cure Light Wounds, Spellcasting minimized), the entire line of encounters risks not being particularly interesting (especially for spellcasters). In "suboptimal" play, it's very easy to make the time critical mission fail. That might actually be desirable, in a way (we want to reward "good" play), but the problem is that both routes don't lead to a lot of fun. Either the individual encounters are perceived as boring, or the party fails in the end.
- Non time-critical adventures introduce the 15 minute adventure day if the party plays "optimal".
Now, some people might not find watching from the side-lines that uninteresting, and see this just as a sign of good play (and after all, the non-spellcasters kick ass!).
And others might say who cares about 15 minute adventure days? It only matters whether the encounters we have are fun and exciting!
In these cases - just don't worry about it. It's not your problem that others prefer to play differently.
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4E tries to remedy this by making a stronger distinction between encounter resources and daily resources.
Daily Powers and Total Healing Surges are resources you have to manage over the day.
Encounter Powers and "Healing Triggers" are encounter resources.
An encounter is already a nail-biter if you have to expend all your encounter resources and your healing triggers. If you're out of Healing Triggers, you face the threat of death, and people will probably have to bring daily resources into the combat to turn the tide of the batle.
The clever use of all powers reward people with the fact that they still have their dailies, which can be reserved for the tougher encounters.
Milestones are an incentive - or a compensation (?) - to continue going. You gain an extra action point, that you can use in a difficult encounter to compensate for a missing daily. (And the various action boosting feats and paragon features make them really effective.). You get extra uses for magical item dailies, letting you again compensate for missing normal dailies.
The system doesn't force anyone to not take an extended rest. (The one rest per 24 hours is irrelevant for this - as others have pointed out, Clerics and Druids could only regain spells at set times of the day, that didn't prevent the 15 minute adventuring day at all. At worst, it facilitated it, because you couldn't rest twice a day to have 3 minutes per day)
If the DM (or adventure designers) throws EL = PL +(3-5) consistently against the PCs, they might still want to rest. Though even then, as long as they have healing surges left (which is likely, considering the total limitations on healing surge triggers), they could go on into "regular" encounters and probably fare well. Of course, most parties wouldn't risk if they have a choice.
The nice thing is, a DM doesn't have to worry if the players do not have a choice - He just makes the remaining encounters easier (EL = PL), and the encounters will still be challenging and interesting.
So, is the problem of the 15 minute adventuring day "solved"?
My answer would be:
For certain values of "solved", it is.
The 15 minute adventuring day is still possible. (Little can change that).
But the implications if you do not follow a 15 minute adventure day are far less dire - the "gamist fun" of challenging combat does not have to be sacrificed for the parties survival chance, or vice versa.
If one wanted to remove the 15 minute adventuring day entirely, one just has to create a mechanic to recharge daily powers and healing surges without resting. Maybe I'll post some house rule ideas on that in some time. The easiest way is of course just removing all daily powers and replacing them with encounter powers, and give unlimited healing surges. Depending on how much you care about the chances of "gain <insert arbritary number> levels in one day" scenarios, this might actually not be a problem.