A few observations I've made (and some that my players have shared with me):
1) 5e doesn't seem to support high level play. Most official products tap out at 11th level. There's little to no help in showing DMs how to craft adventures or encounters for higher level. It's as if there is no intention that characters should play beyond mid level.
As others have pointed out, the surveys have shown WotC that few campaigns go past level 13 or so. Naturally, their materials are targeting the 1st - about 15th level range.
Also, high level play is a lot of work for a DM (and a writer of adventures) because of all the magic the PCs are likely to have at their disposal. High level play requires a lot of built-in attrition of magical resources. I use a bunch of pit traps and chasms just wide enough that they can't be jumped just to eat up lower level spell slots (on jump, feather fall, spider climb and fly).
A high level adventure also pretty much has to be written with the assumption that the magic arms race is in full effect.
Want to keep something secret? It needs magic to keep it secret, and magic to hide that magic from detect magic.
The bad guys better have some means of preventing the PCs from scrying on them or teleporting in and out of their lair. That means more magic.
You might want to make sure patrols have a caster who can dispel magic on that Leomund's Tiny Hut the PCs are trying to rest in too. Yup. More magic.
And, you might consider adding a caster to several encounters just so they can counterspell some of the PCs' spells.
Frankly, high-level play as written is just a huge pain in the butt to run, let alone write adventures for. As a DM, I'd rather start a new game at that point than have to spend at least double the normal time preparing for high-level sessions.
2) The encounter creation math just doesn't work. Some monsters (such as hellhounds) can decimate low level parties. Others are not even challenging at all.
Encounter creation math doesn't work well. The only edition I found it worked well in was 4e. For every other edition you're probably better off using a different method. For 5e my base assumption for an encounter is a number of creatures equal to 1.5 times the size of the party (2 times party size if their AC or HPs are substantally lower than the PCs').
If a monster can hit your party's average AC at least 40% of the time, has at least as many attacks per action as the average party member, and the average party member can hit it no more than 75% of the time, I'd say it's on relatively even footing. Throw 1.5 times the party size of those at it and you've got a relatively balanced encounter.
Another way to look at it is to modify things based on optimization. I have a player at my table who loves to min/max. His wizard bladesinger can achieve a 26 AC with bladesong and shield active. I count that PC as two PCs when doing any encounter math.
Also, the RAW encounter math assumes no magic items. If any member of the party has any magic item that heals them, gives them any kind of resistance, boosts their AC, or their attack and damage bonus, then the math will be out of whack. Personally, I just don't give out +X items, ever. I might be willing to break this rule for some weapons (though I prefer giving them expanded crit ranges or just higher damage dice), but never for anything that boosts AC. NEVER.
3) Most combats are boring. There are few tactical options, and most monsters are just bags of hit points, ever-increasing as characters level up. (This seems to originate from the bounded accuracy design goal.) Most monsters can't reliably hit PC Armor Class.
A lot of 5e monsters lack tactical depth compared to 4e. I steal monster abilities liberally from 4e. I also make my monsters improvise actions a lot. The look on my PCs faces when a kobold rushes them, slides between their legs to get behind them before taking the dodge action, and then another one rushes them and now both kobolds have advantage is priceless.
Here's what I do with dragons in my setting. I'm sure you'll find it rather 4e inspired. And, if not something you want to use then at least hopefully reading it will be good inspiration for you to come up with other stuff of your own.
And here's a hazard and associated monster from my setting. Feel free to use them if you wish.
4) You either have a TPK or no character ever dies. (Not that I like character death, but it should at least feel threatening without being "campaign-ending")
I've found that as well. I think that might be an artifact of the death and dying system 5e uses, because I found the same thing in 4e as well.
5) Few groups (or official products) actually follow the encounters per day guideline, creating overpowered casters and underpowered martial characters.
True, but most 5e official products are remakes of old products who never gave a crap about balancing daily encounters anyway. But, those original products also assumed wizards would have no cantrips to use every round. I like my wizards to always have something magical they can do, but combat cantrips do make them roughly on par with fighters making melee attacks. I suppose one way to deal with this would be to cull all damage dealing cantrips from the cantrip lists. That way a wizard could prestidigitation or friends all day long, but no damage without spending a slot or spell points. Or you could just lower the damage dice of the damaging cantrips to d2s, d3s, d4s or d6s.
I've been watching Matt Colville's YouTube videos, and at his advice, I'm going through my old 4e books for inspiration. I've been redesigning every monster and the encounter math. The game I'm running now is still 5e from the players' perspective, but everything on my side of the DM Screen is homebrewed.
Matt's videos and advice are generally quite good.
I don't think you need to redesign every monster. Just start giving monsters equivalent equipment. At higher level play why wouldn't enemy monsters have +X weapons? As long as the +X equals or is less than what the PCs already have, you're not giving them any upgrades when they defeat the monsters. And why wouldn't goblins suitable for a higher level game be wearing heavier armor? Let's say . . . scale mail. I'm sure whatever high level boss is pitting them against the party can afford to outfit them in better-than-usual armor and weapons.