I don't worry about it at all, and never have. I just put monsters in dungeons or the wilderness or in cities and let the players clash and explore. Sometimes I'll put it ticking clocks or environmental hazards to make resting more difficult.
It's just not something I think about. I'm too busy with "who will the party meet" and "where are they going to travel to", to ever start wondering about how many encounters they need to have between rests.
Random encounters are very random indeed at my table: even I don't know how many of them there will be, or how many monsters will arrive if one occurs.
I don't worry about number of encounters, and other than a very vague check, I don't worry about how difficult an encounter may be according to CR calcs either. I just set things up and then it is up to the players to sort things out.
I voted false... but that isn't 100% true. When we started 5e I used CR and the encounter guidlines... I just by year 2ish found that CR didn't work and the encounter guidelines didn't work for us... so I stopped. I figure 6ish years since I paid it more then lip service is close enough to false.
Random encounters are rolled periodically depending on the terrain, etc. Some days there are none, other days one, and could be as many as half a dozen.
Dungeons, complexes, etc. are "stocked" according to the world and narrative of the adventure.
Players "adventure" according to how they judge their own strengths and weaknesses, but also according to the story itself. Sometimes they need to push, other times they can set their own pace, etc.
Balance is not an issue for me. Only story/narrative/world "building" matters. Some encounters are easy, some challenging, and some meant to be avoided. I don't worry about hit point attrition or such. Characters can rest when they can, but there is no guarantee that a rest will be forthcoming when the PCs are running low on fumes. Players have to be smart about managing their own resources and know when to not push their luck further.
Not once that I can recall. Note that I do try and pay attention to encounter difficulty, insofar as the CR system allows it. It is easier with LevelUp's encounter building rules, but there's still lots of eyeballing.
This poll would be more useful if you also asked "and find monks weaker than paladins".
As ignoring encounters/day just results in short days and very strong per-day classes; so you'd expect if you ignored it to just boost CR higher (or stop caring about it; at 1/day, a group of 5-6 L5 adventurers who bias towards daily classes can take on a CR 20 monster pretty reliably.)