I run more gritty, realistic games so yeah - I take time to track it, but I don't bother the players with it.
If my players are going to spend time in a city they'll go ahead and let me know where they'll be staying and eating regularly since they enjoy roleplaying out these aspects. If they didn't, I'd probably just give them a few options and then we'd ignore it for the rest of the adventure as I would just assume their characters are going back to whatever inn or tavern they chose.
On the other hand, if the players are travelling in the wilderness they'll usually buy some rations before they leave town. I have a 'day tracker' sheet that I use to keep track of time, so I just keep the party's total rations on that sheet. Each time I check off a new day, I check off a day's worth of rations. I don't slow the game down by forcing the players to tell me they're eating (unless, of course, they want to for some reason) as it's just something I assume they do when they 'rest' or have downtime. If the players are in a situation where they're not resting I'll casually mention that they're feeling hungry or tired and won't make a big deal out of it unless it comes to a point where they've been going for a week with no rest or food.
Personally, I think it's an important aspect to the game. It adds another challenge that the players have to consider, and since when are challenges bad?
As if a PC that lived 20 years in a city would forget about the name of the king just because the player did not read the sourcebook, or as if a fighter with years of experience would sheath his blade with blood on it and let it rust just because the player did not know about metal and blood.
It's not really the topic at hand, but I just thought I'd mention that you're commenting on two
way different things here. It's assumed a fighter knows to clean his sword because it makes sense that someone who's been fighting for however long has learned better. OTOH, constantly reminding a player what the name of a King is becomes an annoyance. Maybe I'm just bitter, but if a DM has to do all of the creation work in the first place he shouldn't also have to repeat every little detail twenty times.