Now, in terms of balancing deadliness of encounters, that's what other posters have right. You can do more fewer, more deadly encounters and HP attrition works out. This is important and a big deal. But it's not the only part of this.
The half that doesn't get talked about is the balance of resource recovery models between primary long-rest, short rest, and at-will classes. Plus the hybrids like the barbarian.
Frankly, fewer encounters are a lot less resource intensive than more encounters.
Buffs like Rage or buff spells usually last for the whole encounter, regardless if it's a tougher one. Less resources used in fewer encounters. A barbarian with three rages who rages every encounter is good for all of them if there are 2-3 encounters per day, and half or less of them if there are 6-8 encounters per day.
Making encounters tougher requires either increasing the numbers of foes, increasing the deadliness of foes, or some combination. All of these allow casters to get more bang for the same spells slots.
If it's more foes, area effect spells catch more foes for the same spell slot. It's more efficient.
If it's more powerful foes, due to the nature of saves where a creature will likely have 3-4 bad saves (no proficiency, no superior ability score), while DCs keep going up both from proficiency and from advancing your casting ability score, it is just as easy to affect more powerful creatures as weaker ones as long as you pick a selection of spells to target various saves. So the same slot will now take out more powerful creatures with the same likelyhood. Again, more efficient per slot.
Basically, with how most people - myself included - play, unless we're doing dungeon crawls we're not reaching 6-8 encounters per day, much less exceeding it as often as we are coming under it. That changes the class balance towards the long-rest recovery classes like the casters. Also, extra resources at the end of the day tend to make things feel easier, leading to "easy mode" comments about 5e.
