I. I can't find anything in the DMG that recommends it in 5E the way it is recommend for 4E. So if the players want to take a long rest after 2 encounters: sure, why not. .
The encounter design guidelines call out 6-8 encounters & 2-3 short rests, and a daily exp budget in the 5e DMG.
The DMG for 4e was not specific about the number of encounters per day, though it does go into the number it'd typically take to level, and advised a mix of types & difficulties, the exp budget was just for an encounter.
The reason for the 6-8 encounter norm in 5e is also quite different. In 4e the pacing might have varied with the story and with how well or badly the PCs were doing, those variations would affect how challenging a given encounter was likely be, but they wouldn't much have shifted the balance or drama among the members of the party. When combats were tough, any PC might have thrown down a daily to help turn it in the party's favor, when they weren't, dailies, because there were very few of them per character, were more likely to be conserved. There was a little nuance to managing surges, as well, but, again, everyone had 'em.
In 5e, different characters can have very different resource mixes to manage. Some have few resources at all, that recharge with a short rest, others more, most classes more & more significant daily resources. When you vary pacing & difficulties in 5e, you directly impact how PCs perform relative to each other as well as to the challenges they face. Either sticking to the 6-8 guideline, or varying around it in a carefully tailored way, allows the DM to manage those imbalances to put each PC in the spotlight for a fair share of the fun.
Not everyone plays that way, and if a DM consistently runs a certain way, players who adapt to it - class choice, strategies, etc - or who were just lucky enough to choose a class that ends up favored, will tend to dominate play. For instance, if you regularly blow your daily exp budget on two or three very tough fights, a barbarian with 3 rages/day will be able to rage in every fight. If you tend to have short rests after most fights, and longer days, the Warlock may be casting far more spells per day than the wizard. That kind of thing.
The attribute check on down is designed in 5e to offered a free reign of player options to interact with the environment... (and it’s part of the DM’s job to teach this if the players aren’t fully understanding their total freedom).
5e is very much focused on DM Empowerment, and the free rein you describe is really there for the DM. Players can do what they want so long as a sufficiently unambiguous rule - combat option like attacking with a weapon on a weapon table somewhere, firebolt cantrip, or other spell, etc - saying they can do it. Beyond that, the challenge becomes to declare an action the DM will allow to work or at least call for a roll you're good at. Everyone is on equal footing as far as the most basic humanoid abilities go, but if you have any abilities beyond that, like being able to fly, turn invisible, see in the dark or whatever, then your options, both unambiguous and DM-mediated expand tremendously.