This is an extremely one-sided way of viewing the situation. Does the exploration pillar have the potential to be dull and boring? Yes, though that's mostly down to the play style (if you're running D&D as a game of smart resource use where going over the details of supply and logistics is the whole challenge, then this is not annoying and arduous, on the contrary it's the whole fun!). If all you want to get to is the "fun part" where you can use your flashy abilities and fight setpiece encounters, exploration is supremely boring. Admittedly, modern D&D has gone quite far away from old-school exploration style, where things like spell slots and use limits to abilities were mostly about resource management, they're now about having cool setpiece battles. But these vestigial rules still exist, and there's a (fun!) reason for them to exist, if you run your game accordingly. All the "annoying and arduous" bits of 5E's rule system, such as managing your inventory, picking minor adventuring gear, checking for random encounters every 20 minutes etc. is part of the core gameplay loop of OSR games, and these games seem to take essentially the same rules as 5E and make them much more interesting. So I think calling exploration annoying and arduous and only something the DM enjoys is unfair.
However, the DMG doesn't teach you how to run exploration as a challenge of logistics, and most people's sensibilities run counter to that now. So Exploration is either this weird timesink that the DMs have a hard time running (because nobody told them how to do it), or you just want to skip over the details ("You make it to the next town where the quest continues..."). The problem that
@Micah Sweet has pointed out is that Ranger and Outlander backgrounds imply in the game's fiction that you're a master of these challenges. Logically, people who enjoy the part about surviving in the forest or arduously tracking an enemy would pick these classes. But these specific options that cater to the exploration fantasy are the same ones that nullify that pillar - a party with a ranger never gets lost, and an outlander always finds enough food. So there's a massive mismatch between the kind of people who'd like the specific option's fantasy (people who want to run exploration in the old way, or something close to it) and what the option does (make exploration completely obselete).
I think it's very much possible to have an exploration pillar in 5E that isn't annoying and arduous, it's just that WotC doesn't bother catering to that audience anymore. Which is a shame, because completely ignoring that pillar makes some of the design choices that were holdovers from earlier editions even weirder, when these choices could be developed in a way that's fun for everyone.