How do other DM’s handle this? On the odd occasion that the use of door bashing is needed I just assume the party eventually gets through, calculate how long at average damage it would take to bust through a door and leave it at that. This assumes they cant just break the door open. So in the end it just adds some time to the groups travels but time isn’t that important in many occurrences.
My group also tends to always take 20 on searches which can mean hours for large room.. Again not that important for non-time restrained adventures. I am tempted to throw in a random encounter but they don’t do it enough to warrant it just yet. Though it is a tool in my arsenal.
I take care of it pretty much like you do. 2 minutes per 5' space if it matters for spell duration and average damage if it matters for spell duration. If it does not matter then I just say something along the lines of 'eventually you batter the door down and...' or 'eventually you finish searching the room and...'
I generally avoid random encounters. I kind of view them as plotless bonus XP that usually showcases a fight that is not actually as interesting as one that might occur in a well planned adventure. Pretty much I can't really think of much in the way of their good points. I keep in mind the habits of the monsters that live near by and they might stumble on the PCs but I rarely actually use pure random encounters.
I've given up as far as putting doors in my dungeons, because my group doesn't tend to like the idea of the Open Lock skill. Just bash and go. There is no respect for the architects of ruins, dungeons, or even homes... unless the owner is present and willingly cooperative, in which case doors are opened for the party anyway.
If I'm going to put something that can be locked in my game, you can be sure there's a penalty just waiting for the PCs to start bashing. For a chest, potions inside may audibly break. For doors, monsters may hear the pounding on the other side and prep an ambush. If I'm really feeling hostile, the trigger for a trap may just be bashing a otherwise useless door down. Basically, if I am using a lock in game it means that there's an encounter coming up that would be far easier if the lock was picked - otherwise its just a few rolls of the dice for no reason other than to suck time away from the fun parts of the game. No one wants that.
On the Search via take 20 strategy, I generally don't have a problem with it. I do make a point to tell the group approximately how long it takes, and occasionally have unintended consequences pop up - the tide might roll into the entrance, preventing escape by conventional means, or a PC may have a scheduled event that he misses due to losing track of time. One thing I like to point out is that the majority of buff spells don't last all that long, so the players have a choice: either search now and risk running out of spells when the BBEG finds them, or clear the dungeon using as few of their magical effects as possible and risk something or some rival taking their earned treasure from under their nose.
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On the Search thing, I tend to houserule that Spot can work in some instances (like seeing that the mattress has a bulge in an unlikely spot indicating that something may be up) and just up the DC of the search by 5 for spotting. Some party members get searches going, while others scan the room. If I wanna speed things up I just have the spotter see the outline of the secret niche which holds the loot. I like it even though it may or may not be too easy and I usually lower DCs at higher levels (how in the world is finding a magical longsword in a room a DC30+ search check?). I don't like creeping DCs that D&D has, if you keep you skill up you always have the same chance of success. How is that getting any better as I level up? Basically I just try to keep the game rolling and I assume that the party will find the treasures (that's why it is there, right?) so I use descriptions to indicate that they found a well hidden treasure: "The seam you spot on a battered tableleg seemed out of place and upon further examination you discover that the leg splits into 2 halves longways, revealing a small hollowed out chamber. Inside the chamber is nestled a glowing necklace of exquisite beauty." sounds much cooler than: "Your 45 minutes of searching the room uncover a glowing necklace of exquisite beauty." and keeps people immersed in the PC's world more.
Thought I would share.
FH
Door bashing is generally avoided IMC, It give whoever is on the other side plenty of time to prepare and there is almost garenteed to be a random encounter at your back just as the action starts.