I hate when guests overstay their welcome and assume it's nothing to you. You pay for your stay and anything outside of that is a "favour."
I had a trend of guests doing the same thing, but I'm not able to cater for this because I'm always back to back with bookings. My apartment is too small for past and present guests to intermingle... And I need time to change over the room.
Since I got annoyed by these requests, I did a few things. Now - all of my guests leave either before time or exactly on time. My anxiety over this, is now totally gone. This is what worked for me:
1. State in listing "CHECK-IN is 12 midday and CHECK-OUT is at 11am. If you need luggage storage before or after, you can go to 'XYZ Storage' on 'Bla bla' Street for a small fee."
2. In the booking confirmation message, state the CHECK-IN time. Then ask for a precise arrival time AFTER that (eliminates guests asking to store bags earlier than your check in time).
3. Print out a list of house rules and put it in a frame underneath the WIFI password. (This way, they can't NOT see it, because they always need to look for the WIFI password). In the house rules, state again the check out time and - again - offer an option for an alternative luggage storage place. Make sure to drop the word "strictly" in there somewhere too.
4. On the last night, thank them and tell them how the check out process works, then politely remind them of the CHECK-OUT time, "as per house rules".
Honestly, before I did all this, every second guest was asking me if they could store bags. If you state your boundaries clearly and over and over... There is no way they will chance their luck. You stomp it out before they get the chance to do so. And I found it doesn't have any affect on my hospitality ratings (touch wood)... Hope this helps!! best of luck