I'm going to disagree, but not fully. 5e doesn't provide robust approaches that some other games do, but that's not a failure -- it's on purpose. D&D did originally expect the GM to be a game designer, using the rules as a primer or inspiration to make their game their own. This lessened somewhat in AD&D (both editions), but still provided a system that was expected to be customized by the GM. 3.x broke away from this by providing much more player-side focused play (with clear, expected rules for almost everything), which caused it's own set of issues because they didn't address the fundamental assumptions of GM designed play and just forced a single, main approach. 4e, interestingly, was as player-sided as 3.x, but did fix a lot of the fundamental issues, so it worked better (if you grokked the fundamental changes, which the designers did a poor job of explaining until much later in the 4e cycle). 5e has reversed course, and is back to providing a toolkit for the GM to, ultimately, design their own game. So, combat is very much an area that 5e expects the GM to do the work to tailor it to their table, and we agree here. Where we disagree is on this being poor design. I don't think it is -- it's very intentional and part of why I think D&D maintains it's overwhelming market share.
Here I'm going to disagree hard with you because you are under the mistaken impression that player sided vs DM sided is a zero sum game.
3.X is player sided
and anti-DM. This is because 3.X RAW tells the DM to use the same rules the players do. A good example here is feats. Being able to browse through the rulebook and pick two or three feats to add colour and mechanics is superb for many players. On the other hand having to pick two or three feats out of the 1500 or so available for every minor monster is tooth-grindingly fiddly and obnoxious. As is the hard coding of spells rather than doing what you want.
4e is player sided
and DM sided. There were slightly more feats available by the end of 4e than by 3.5 and far more customisation available. But a fundamental difference here is that
4e DMs are not told to follow the same rules as 4e players. The two roles are considered very different so what you do is different. As a DM in 4e I am actively significantly more empowered than I am in 5e; I can do whatever I like in both games - but I have better tools and fewer constraints to do it. If I want to be a game designer in 4e I can be - the only key difference is that the baseline is much higher so if my game design is crap it will stand out like a sore thumb.
5e on the other hand isn't
as player facing as 3.X - but it's less DM facing than oD&D, AD&D 1e, or 4e. If I want to run the game by the intended rules and just design my own monsters 4e is so vastly superior in its benchmarks it is silly. If I want to customise areas or create house rules there is no fundamental difference in doing so.
And if I want combat straight out of the books then in 5e I get bullet sponge enemies, minimised tactics, and a much less swingy game but with combats that are little different in length to other WotC editions.
You still haven't explained why it is a
good thing that the DM, in addition to running the world, running the NPCs, and playing the adversaries in combat is also supposed to be a game designer when they laid out probably $150 on a supposedly functional game. Some DMs like to be game designers but not all do. So those that don't like to but have all the other skills required are close to locked out.
And there is a good reason that every single 4e game I have played has at least 50% of the players ready, willing, and able to DM. 5e isn't in my experience quite back to the dark old days of 3.X where groups fell apart because no one would or could DM. But the load is higher on the DM and the tools are worse while the 4e DM has IME significantly more power because they can decide how spells will work rather than these being hard coded by the rules and with a pretty set paradigm.
They do different things, and I don't think you can have the flexibility and strong vision story of D&D with one of those combat engines.
You say "strong vision story", I say "railroading". And flexibility is something we'll have to disagree on. But yes, I agree that if you want a linear story directed by The Storyteller and in which the stakes are defeat or victory then the post-Forge games like Fate Core, Apocalypse World, or Blades in the Dark aren't good. But when the stakes of combat are laid down in advance (as they are in this style of play) then the slow combat that lacks tactical depth because positioning is of minimal importance, and that lacks danger because hit points don't inspire death spirals does not help.