I don't know about "good chance". Small chance, perhaps. I've still never had a package stolen in 20+ years of ordering online. But many folks have packages delivered to work for this reason (and I admit I'm more likely to have expensive packages delivered to work). But the lockers solve a problem I don't really have, and suddenly make ordering online as inconvenient as buying stuff in-store.
I have a place in suburban Minneapolis and I could (and have) left packages sitting on my doorstep for weeks while on vacation. Still there when I got back - only a single lost package over about a decade now.
I also have a place in Chicago. A package left outside at the door would be gone within hours as I live directly off a very busy street. Even if put inside, if the door gets left unlocked or ajar a bit you have a very high chance of the package disappearing. Packages get delivered to the office or not at all when I'm in town.
I agree re: having zero interest in driving to the nearest locker though - I'd just go to the store. It's possible they will reach the density in Chicago where I can walk a half block - which I'd be okay with - but I can't imagine that being cost effective for most areas of the city.
Somewhat OT, but are these common in US (or wherever you are)? If so, out of interest, what other duties to they have?
In Finland, I've never seen such offices even in the larger apartment buildings with hundreds of dwellings.
Parcel lockers (both public and recently in apartment buildings) are a thing here as well, but they are mostly replacing pickup-from-post-office. Home delivery has always been a premium option when ordering online, not the norm. The network here is owned by Posti so any company or individual can send packages to them, or use them to send packages at cheaper rates than going to the post office.
Heavily weight the first impressions of the leasing / office staff to determine whether you WANT to live in an apartment complex: As stated above, these will be the people you will deal with for anything from clogged drains - to being unable to pay rent on time.
In short: you want to make sure they are friendly, professional and courteous -- or it may ultimately detract from the perceived quality of living in that Apartment [0].
[0] - I lived in 6 apartment complexes from time I was a broke student to young professional with a family.
But if a rental provider company owns the complex outright, they still don't have building-specific offices, but just one central office per city/region.
While such an arrangement is possible and legal everywhere something like 95% of all co-ops are in New York City.
The USPS does also have package lockers - larger boxes with keys that get left in your mailbox - but they aren't universal and companies like Fedex and UPS rarely have access to them. You can also have things held at the post office.
It's not that there are no other ways of solving the problem, it's just that the lockers are convenient and requires very little planning or forethought.
So what do you do if you need a strip of LEDs for a project that you're putting together by this weekend and you don't have the right hours open in your schedule? (Or [insert random product here]?)
Just have it show up at the supermarket/drug store/gas station in a couple of days. Easy.
It's also cool that the apartment buildings can install the lockers and use them for packages which Amazon never touches, for the whole 'business hours' problem. But as Amazon's programs for offering free shipping to 3rd-party sellers are making it more of an 'Everything Store' by the day...well, it'll definitely be interesting to see what happens.