They become tedious slogs because the battles don't really matter. Why are we fighting? Because we're supposed to have X fights per adventuring day. When the system is designed to have X number of fights, at some point you're going to run out of reasons and fights will seem contrived. In a lighter system, this isn't a problem because combat is a breeze. In a heavier system like D&D it can become a chore.
You are absolutely not getting what I am saying.
Imagine the final battle of a campaign. It has been 20 levels of adventuring in the making. A powerful spellcaster is in the heart of their base and is casting a ritual that will change the face of the world in a nightmarish way - and the PCs want to stop it. They have to get through waves of enemies just to reach that powerful spellcaster.
Option 1: The DM just has the enemy attack the PCs to kill them. Wave after way. Attack. Breath fire. Tail Spikes. Disintegrate spells. Blah, blah, blah.
Option 2: The first wave of enemies open up with a Scatter Spell to split up the party and contain them. Then, they use Wall Spells, to slow the PCs down and prevent them from getting to where they want. Enemies know the enraged barbarian can't be grappled and is essentially immune to hold monster - but he gets Banished and another PC has to track down the caster and break their concentration to bring the barbarian back.
A REALLY good DM can make either approach good, but it is a lot easier to make the second option interesting and engaging because the challenges are constantly shifting. You're not just dealing with probability and erosion of hps - you're dealing with tactics and strategy.
This isn't just a 'from the air example' - this is an actual final battle of a campaign I ran. The enemy knew that all that mattered was delaying the PCs, so all they did was delay them. They didn't try to kill them because it was too hard. Instead, they tried to slow them down. The PCs found ways to bypass the defenses, to turn my 'traps' into benefits, and eventually to get into the endzone and kill the BBEG. However, almost every round of combat as they fought their way through the gauntlet was different - and the bad guys focusing on slowing them down, rather than killing them, was noted by the players. The player that called it out said, "and it makes sense ... they know they can't kill us." In other words - the 20th level heroes felt like bad @$%es. It was a really awesome final culmination of the campaign - and no PC ever dropped below half HPs.
Think about comic books. They tells stories about heroes, too. Sometimes Spider-man gets beat up. However, sometimes he kicks butt and doesn't even get a scratch. Those are the moments that make you think of him as a competent and capable hero - and they can be fun parts of the story as well.
If you think battles with objectives other than a deadly challenge are just tedious slogs, you are absolutely missing out on great opportunities to make your game better.