When he was sick those existed but were still pretty expensive

For sure, it's much more of an option now.

Particularly because occasionally he would have a different nurse. Something would happen and last minute they’d have to send someone other than the usual 2-3 that would come. So they’d have the code on his file.

Same concept with a keypad lock. Create a code for the nursing agency, and have them put it on file.

The box he had locked onto the door handle, so it would have been a good option for someone that rents and can’t necessarily change the lock on the home. Or someone that just doesn’t feel handy enough to change a lock themselves.

Absolutely. Even with keypad locks being more common/cheaper, a real estate style lockbox is still a good option.

What I don't like about the real estate style lockboxes, is that they give access to the physical key.

Suppose there's a nurse that comes by regularly. The nurse knows that the homeowner has some valuables (that the nurse wants to steal) hidden or locked up in the house. The nurse also knows the homeowner is going to visit family for a few weeks.

The nurse can get the code for the lockbox - no problem, they're an authorized person. Just before they unlock the door, they use a $15 key guage and write down the key's bitting (the measurement of the notches on the key). To any observer who isn't watching very closely, nothing suspicious happened.

The homeowner, when they go visit family, brings the lockbox (and the key) inside the house. They think their house is secure. Nope! The nurse (who measured the key's bitting) went to a locksmith and had a key cut. The nurse waits for the homeowner to leave, and then has a few weeks to find the valuables. Observing neighbors would simply see the nurse (who has been there many times before) use a key to go into the house (which they have seen happen many times before). Only people who know the homeowner is out of town would suspect something - if they happen to see the nurse entering, and realize it's suspicious. Additionally, there would be no signs of a break-in, which would make it harder for you to get any results from police, and harder to get insurance payouts.

With the electronic door locks, regular nurses would get their own dedicated code. The staffing folks would have a code for any temporary folks, but that code would be regularly changed. The codes can be temporarily disabled when the homeowner goes out of town. Additionally, many keypad locks provide auditing - you can see exactly when each code was used. The nurse would be left with more traditional, noticble, or time consuming approaches, like breaking windows, picking locks, etc.