I'm not the person you quoted, but the reason I would find that hard to believe is true is because it is staggeringly restrictive and any design that depends on that to more than a very casual degree is flawed. Why flawed? Because it should be possible to design a game that functions just as well for a much wider range. No other role-playing game I have ever played is as restrictive as that and to my mind the purpose of a role-playing game is to tell stories. Monopoly - a game of chance and arbitrariness - is about the last thing that should be a point of comparison for a role-playing game. For a role-playing game to be so focused on progressing through a set amount of encounters per day rules out any sort of story where encounters follow naturally from events and decisions rather than from metagame reasons. That logic is almost by definition. I'll repeat it because it is a critical flaw in a role-playing game. If the game system pushes you towards a set number of encounters to work well, then encounters are not following from player decisions, from the flow of the plot or the story or drama. They're being set by meta reasons and the story, drama, player decisions are all being driven by rules reasons rather than in-game events. That is a flaw because it reduces versimilitude and constrains many types of stories and player decisions. Constraint without advantage is an objectively bad thing because some lose for the sake of nobody gaining. If making a game work for six encounters by necessity made it work poorly for any other number of encounters, that would be one thing. But it doesn't. No other role-playing game I have played is so limited.
I am not comparing the type of game. Yes D&D is a roleplaying game and Monopoly is not, but in the end they are both games based on a set of rules and assumptions. If you do not follow the rules or change the things the assumptions are based on, well then it's not gonna work whether its D&D, Monopoly, Shadowrun, or friggen chutes and ladders. You either play the game as intended or you do not, in which case you need to spend the time to tweak aspects of the game to fit with how you are playing it. Game type is irrelevant. Either play it as designed or spend the time to make it work for how you want to play it, they gave us all the tools to do it either way.
So there really is no 'correctly.'
A system doesn't need to be perfect to avoid falling apart. And, you can have things like Polymorph or Teleport without having problematic 3.0 Polymorph or scry/buff/teleport. Besides, still holding together up to 15th is arguably better than 3e or the classic game did.
There absolutely is a correct way to play it. Build your game with 6-8 encounters, use legendary creatures and Lair actions or at least play the creatures properly using the abilities they have in a strategic way. Had he done that the OP would have had a much better experience, but instead he decided to do none of that and then complain how the game is broken. The game is not perfect, but it's pretty dang good when you play it right. I personally would like more high level monsters and a few tweaks to high level to make it work better. I would prefer it built on less encounters a day but just because that is my preference, doesn’t mean the game is broken. But throwing a half arsed handful of creatures at a high level party then not using their abilities and playing them well will never work, no matter what system you use. Any edition or RPG you play will fall apart if you toss a bunch of high level creatures at the party and then not use their abilities, they have those abilities for a reason. That is my issue. You can call me an apologist all you want but in the end my games run just fine with the tools we were given whether it’s me using the rules to custom design things or just dropping things in. I just don’t see that anything is broken. It may not be optimal for how I want to run it but that doesn’t mean it’s broken.
I'm sorry but "no thing can be perfect" is actually false. Why: because it is the perfect example of a bad argument!
(As if we demand perfection, when we only want to hold the designers responsible for making easily avoidable flaws that in some cases are even taking steps backwards compared to before.)
But seriously, it really is nothing but a bad-faith argument. By the way - "that's why there is a DM" is also an old chestnut of equal caliber.
I'm pointing these things out, not to single you out mpwylie or argue against you, but to illustrate two perfect examples of arguments that doesn't explain the state of affairs, but excuse them.
This is a game that thousands of other people are playing. No system in the history of mankind has been or will ever be perfect for everyone. But fine, we can ignore that as an argument. The fact remains that this was a single encounter run in a system designed to be 6-8 encounters a day. These were creatures with spells and abilities that where not used optimally against a team of players that are playing optimally. That is not a broken system, that is a DM failure.
And the old chestnut of “that’s why there is a DM” is exactly correct. As a DM you should know the rules, know the abilities of the creatures in your encounter, and if you do not follow the system as designed, tweak the encounters to account for it. D&D is a base system for the masses and there is a DM to use the rules, options, and creatures to tailor the game for the group playing.
In the end all I am saying is that you can’t run the game in a way which it was not designed without putting in the hours to make it work. I am there with you, I generally do not run it the way they designed it, I do not like the assumptions that it was built on. But I know that it is my choice to not follow those design assumptions and because of it I must spend time and effort to make it work. This is specifically why I follow the design assumptions for my second group, cause I don’t have the time to commit to custom building things for 2 groups. And again, both of my groups run fine, one because I am spending the time to custom build stuff to not play it properly, and the second because I am following the design which demands almost none of my time past reading the spells and abilities of the monsters I use. If you want to hold the designers accountable, then you as a DM need to be accountable for correctly using the system they designed. If you run 6-8 encounters per adventuring day and play the creatures competently and they still cakewalk through it, THEN you can hold them responsible. Until then this entire argument is in bad faith.