Most DMs don't plan for getting to that level so they kind of get blindsided by the players' power. Preparation is also more time consuming if you go to every nut and bolt. I personally rarely do a full build of my NPCs; fights only last a half-dozen rounds so I only need to know their combat-related skills, say a dozen different spells for the fight and another half dozen or so as pre-fight buffs.
Plots are also different. Dungeons become pointless as such. I got out of the dungeon rut when my game started at 1st level by explicitly avoiding them if at all possible. Oh, they explored a lost city, snuck into a demon infested castle, stalked a beholder underground and invaded a massive graveyard, but those are about the only "classic dungeon" scenarios in some 6 years of gaming.
I try to keep the physical scope of the plots large. Maybe not individual plots, but I have multiple plots active simultaneously (about 10 threads now) and they aren't all in the same place. I create time crunches not by limiting their ability to travel but their ability to be in multiple places at once. Their Leadership is almost exclusively used to handle all the "little things" that they can't be bothered with.
The greatest thing I ever implemented was the Laws of Unintended Consequences. The first law is that for every action there are at least three completely unanticipated consequences. The second law is that the scope of the consequences increase exponentially with the importance of the action. The third law states that events of almost infinite scope can be triggered by apparently minor consequences. The 3rd Law is also known as the Tacoma Narrows Bridge Law.
So if the players kill a local bandit chief there will be multiple responses, the most likely being the favor of those targeted by the bandits, being recognized as a potential threat by other bandits, and probably at least one individual who is either incredibly grateful to the players or hates them very much. These consequences stack up and eventually the plots start writing themselves as various factions in the world have become aware of the party and begin to include the PCs as factors in plans and goals. It's a feedback loop, where NPC actions beget PC actions which themselves beget future NPC actions. It actually increases immersion as the players can often figure out that Z happens because they did Y. Furthermore, the players begin to ponder the impact of their deeds down the line, which in many cases is enough to prevent much of the player foolishness that destroys games.
However this requires planning from the get go, or at least taking enough notes of the events to be able to have the ripples form at the right times. It has to be present pretty much from the beginning and include both good and bad consequences or the players will feel that you are just beating up on them and the plots will feel forced.
I play pretty close to the RAW treasure guidelines and use those unexpected good consequences to help smooth things out. When the PCs are falling behind for whatever reason, I might have a noble reward them for some past deed. "I, the Duke of Adventure#3Land, was visiting my cousin the Count of Farawayland when the dread monster plagued my lands. I thank you for slaying it when my vassal, the Baron InneffectualNPC, was unable to muster the troops. Take this chest of gold as a sign of my favor."
Later I can have the Duke of Adventure#3Land contact the PCs to deal with some relatively big problem, suitable to their current level. The players can also consider petitioning the Duke for assistance with their problems. Smart players will ask for letters of introduction or explain how their current quest could aid the Duke in the hopes that he Knights them or otherwise grants them some sign that other nobles should take them seriously.
This isn't standard D&D modules though so it isn't common. In 1E you had the name levels, where fighters acquire castles and the like, that was supposed to guide the Dm towards such world-integration but it never really caught on. I really wish more DMs would read fantasy novel series that cover long periods of years. Raymond Feist's game was pretty over the top but it spanned decades of game time and the players gained in physical and social power. Look at young Pug, awarded a minor manor in return for saving the princess. While a bit overboard in D&D terms, similar kinds of giftings should be more common.