What is the real problem
I think the problem isn't the standing orders themselves. The problem is creating the need to issue them!
You have to ask yourself what exactly you're trying to achieve by not allowing players to issue such standing orders.
Let's take the arrow gathering example. Do you really want the players to go through a checklist after each fight? "We have looted the corpses, gathered the arrows, blessed the ground on which bloody skeletons were slain, looked for hidden treasure, cleaned and bandaged our wounds... Whats left on the list, Steve?"
Sooo, we are doing the same thing for the 100th time, eh? Guess our characters could have learned to do that themselves, without us telling them to each time...
This is repetition, and repetition is bad, both in programming and in storytelling. Gathering arrows, replenishing your poison supplies, selling the useless but valuable loot in the city... Or taking a piss when you feel the need to, making a fire when you're camping, etc, etc. All these are mundane things, absolutely not worthy of a players declaration. Such things, if there is a need to handle them, should be described by the GM, and the players should have the right to protest such a description and act differently if they wish. How bored would you be reading for the hundredth time how Aragorn hunted for food and Legolas gathered his arrows? Would you like to read about every single meal the Fellowship of the Ring had on its journey? I wouldn't like that at all!
Example from my own experience
In some of the games my friend did GM, I really disliked those parts, where nothing really happened and we were left to mundane tasks and doing-nothing. Declaring that "I'm making a campfire" "I'm keeping watch!" "I'm making new ammo!" "Errr... I hone my knife!" and describing the effects of those actions... It took considerable time and wasn't all that interesting! It could be waved off by a brief description and, with a bit of research beforehand, the description could be actually interesting! Like: "You made camp and did your regular duties. Funny thing is, you ran out of dry meat, yet no one noticed -- Mike always cooked badly, and he just happened to catch a few rats running around while he was cutting the carrots..."
Later the GM kept us describing taking turns at the watch during the night, just to see who will be the one making a roll for detecting the enemy sneaking in. Boring! He might have said we were sleeping and make roll to see whose watch was it when the enemy came... If anyone wasn't going to sleep through the night, he could interrupt the GM when he said "you were all sleeping".
After each fight we would describe: "I loot this guy". The GM would say "You found X". Then Someone would have to declare "I loot that guy". We would find Y. We would have to gather shell casings for our ammo to be refilled (low resource post apo setting called Neuroshima). Declaring all this and hearing the effects is boring, as it's always the same, mechanical, mundane. There is no story nor roles in it, and this is supposed to be a roleplaying/storytelling game! A description would be shorter and more colorful. It may even be conducted by a player!
It's all down to INTERESTING decisions
The game of roleplaying is about decisions. "Will I loot the corpse or gather the arrows first" is not an interesting decision. "Will I take the 5min to gather my arrows" isn't one either, unless you have a gang of hungry orcs chasing you. "Will I sell this crap sword to the one merchant or another" is not an interesting decision. But deciding whether we stay in the city to replenish our supplies, rest etc. or do we leave immediately cause we fear that [insert anything]" is a more interesting one. Once the players decide that they stay, don't make them do chores and mundane tasks. Have the players accustomed to the notion that if you give them the storytelling when there are no big decisions to be made, they should use it to build dialogs and relations with the NPC and other players, they can do some roleplay, have some fun. That they don't have to be busy doing mundane stuff, cause you'll take care of that for them.
What about the traps?
Well, we have to think about - what is the player trying to achieve? Well, he wants to reduce the redundant blabber! He does not want to explicitly state that he is alert, and he does not want to be told "you saw nothing cause you didn't look for it". So you might as well talk with him about it. "Okay Joe, your character is pretty alert. The dude always looks for escape routes once he enters a room, kind of a part of being a rogue. But that's not the same as going step by step knocking on every stone or log in the wall. So if there is anything of note in the room, I'll make a secret alertness roll for you, and if you succeed, I'll tell you to roll on your traps or whatever skill. If you fail the first roll, only an active search will let you roll on traps. It's this or going everywhere crawling and looking for traps...". Joe should be pretty content with that and have a feeling that you won't screw him over, cause he didn't want to declare the same action every time, everywhere. This is the advice others had already offered here, but my point is to accentuate that it gets rid of the stupid repetition. Also, my point is not to make it sound like a "well, this rule says you can't, even though it would be a good idea/make it harder for me to screw with you". If it sounded like that, it would help keep the misunderstanding that the GM is against the players, while his real role is to provide challenges for the players. Without challenge, they'd get bored after the first 15 minutes! But the challenge should not rely on their mistakes, rules "gotcha!"'s and similar.
Don't make it a fight with the players
TL;DR: I don't like the accepted answers notion to argue with the players and shut em off with " Yeah, sure you can keep a crossbow loaded all the time. Guess what? You're not going to be able to fire it because it will jam or break or go off by itself.". It said that the problem is with player expectations and I agree, but the answer didn't seem to explore this concept all so much. Do you really expect the players to always declare the same boring things just because they don't want to be spending their gold on new arrows even though they could simply pick the whole ones after a fight? Do they expect to get to the interesting stuff, skipping the obvious? All in all - let them have those standing orders. They're nothing bad! Actually, they can be good for the story and the game itself. The players do these things to make the game more enjoyable for them, not to fight/annoy you.