I'm not at all saying that you couldn't have that thrilling dungeoneering action sequence in 4E (although you might have to houserule the part where you forestall an encounter with a web spell - previous editions have lots of spells that could be useful in combat but we frequently use to avoid fighting, which 4E has eliminated).
What I am saying is, like Dasuul implied, each of those is a different activity in 4E. There's a whole system for combat, and to keep playing that system from getting monotonous you need to break it up with some play of the skill challenge system. Moving from one kind of play to another involves setup time - now we draw the battlemat and determine initiative order, now we announce which skills can be used in the challenge and set the stakes. What that means is that you're still best off moving from one setpiece to another, with the dungeon being the backdrop between these separate scenes of thrilling action.
In TSR D&D, it's all part of the same system. The point of my example wasn't that cool things happen, it's that you go right from one to the next with no delay due to set-up time. It takes about as long at the table to fight a combat as it does to search for an exit, and the game treats both the same way.
Another way of saying this is that the mixed-up sequence of fighting, running, and exploring is kind of the norm in old-school megadungeon play because it works with the mechanics. Fighting one round of combat takes a minute, and so does moving 90 feet or searching for a secret door. Deciding how you spend each minute is exciting because it brings you that much closer to the point where the DM gets to make a wandering monster roll or check to see if you run out of lamp oil.
My experience as a player and DM is that trying to play this way in 4E is less fun because it goes against the grain of the mechanics. A string of fights without rest isn't just monotonous: each combat is less fun because not refreshing encounter powers robs you of choices and puts you in the at-will grind. And if the wandering monster that kept you from resting is just a nuisance (which is the point, otherwise you'd just bang pots until an interesting enemy laden with gold came to fight you) no one is going to be happy that you've just spent an hour dicing out this boring combat. I'm super interested in things like a social or exploration skill challenge mixed with combat, or a way to handle strings of combats and wandering monsters. But I want to learn more about that stuff precisely because I find it so difficult to have 4E do that well.
There are tons of things 4E does well that are hard to achieve in old-school D&D, like choice-rich tactical combat and social encounters that don't boil down to real life factors like who is the most persuasive (best case) or well-liked by the DM (worst case). I'm just saying that free-flowing megadungeon play is something that people did back in the day, and use older rules to do nowadays, because the rules support it in the way 4E supports dramatic scenes with cut-scenes between.
EDIT 1: In 3E as players my group already treated big dungeons as setpiece battles - we'd scout, retreat and buff, and re-engage at lower levels, and scry and teleport at higher ones. I think that was an unintended consequence of making buff spells powerful, plentiful, and long-lasting enough that you could get in and out before they ran out, but it probably did help create a playstyle that 4E consciously designed around.
EDIT 2: I talk more about megadungeons in 4E
at the Mule Abides, which references the older EN World post that that's an expansion of (and which has many good ideas that aren't mine).
EDIT 3: Web in 4E is a useful attack spell that contributes about as much to the outcome of a fight as any other character's power of the same type and level, as it's supposed to. Web in OD&D is a crazy spell that is potentially useful in combat if you want to get real close and are very sure that you aren't going to trap or isolate any of your friends, neither of which is usually true. However, it's great for sealing doors when you're scared to death of the things that are about to come out of them. There's nothing like that in 4E because sealing doors would be a ritual, which means it would take ten minutes; only one character could do it, so if that PC's player didn't show up and you'd planned the adventure around the party being able to seal in the Glabrous Death with a web, it'd eat everyone; if that one character ever did manage to use it effectively in combat, everyone else would complain that they had the "I win" button; and fighting is supposed to be fun and a central activity of play in 4E, not something ridiculously lethal that is best avoided if at all possible like in OD&D.
