Why do some hotels ask you to leave the key at the reception when you go out to come back later?

Some hotels do like the keys to be left at the premises. That is just the way it is.

It is more work for them, to collect the keys and hand them back whenever you want to go to your room.
But they think it is worth it.

I have seen this when the keys or the keyfobs were quite expensive and in old fashioned/traditional hotels, where service is still valued.

All hotels have either a spare set of keys or a master key, or likely both. So no reason not to service the rooms. But hotel staff have told me that if the guest forgets to hand in the key when leaving, they have to have a new key made, which is a nuisance at least and can be costly in the longer run.

In addition to the existing answers:

In budget hotels, it can save yet another bit of cost as they don't need to give out multiple keys per room. This has multiple advantages:

• The cost of making the extra key
• The hassle if even 1 of the keys gets lost
• Because it is 1 key, you can force people to turn of the light when they leave the room (as they need to insert the keycard to make electricity work)

Why do some hotels ask you to leave the key at the reception when you go out to come back later?

In the past (1970's/80's), for smaller hotels and pensions:

• prevention of loss (they were rather ugly and heavy for a reason)
• prevention of strangers 'wandering' around, where the reception is strategically placed near the main/only entry
• telefon calls: with the then existing older systems where a manual connection was required, one simply told the caller that the guest was away if the key was there.

Hotels then often had a 'long memory', so people working there were often trained on what to look out for.

Maids would report to their Matron/Housekeeper and they would report to the receptionist anything that looked odd (the main source of the hotel grapevine that was very fast and often more extensive than strictly necessary).

Often, someone in the hotel knew how to exchange locks (and other general repairs), which would be done if a key was lost under suspicious circumstances. Thus a stolen key would no longer match the original room and become useless for a hotel thief. In the small hotel I worked at during my studies, the owner did this himself keeping track of all the exchanges. There were also spare keys/locks, so it could be quite some time until a stolen key would be used for another room.

So there were good reasons for this policy, which served not only the interest of the hotel but also of the guest (in public statements: the other way around).