Do I feel "more safe" if I get buzzed into a facility (doctor's office, in this situation)?
Sort of ... Maybe ... It depends ...
Obivously, the fact that it exists indicates that the general area is risky, so while it may be a tad safer inside, it's presumed to be riskier outside, where I'll eventually have to return to car.
Once inside, it may be "safer" or not. If the person who operates the buzzer merely pushes the button everytime someone hits the doorbell, and indiscriminantly lets folks in simply because they "ring the bell", then there's no real improvement in discrimination of who enters. If the employee/attendant is diligent and uses a speaker system to first indentify the bell-ringer, it could help improve security.
Example 1: person rings bell, attendant pushes buzzer and lets someone in. This doesn't really improve security.
Example 2: person rings bell, attendant talks to bell-ringer and asks "May I help you?" or "Do you have an appointment"? Once the bell-ringer answers, the statement is checked against the expected patient roster; admittance is based on a properly accepted response and not just a blindly pushed button. This would improve security.
Adding in visual affirmation would be yet another improvement. Either direct visual confirmation or a video system. If the bell-ringer states they are the Fed-Ex person, and you can see a uniform and package, that help's verify the claim. But if the bell-ringer states they are UPS, and they're standing there in tattered street clothes and pushing a shopping-cart, that's a red-flag and cause for denial of entry.
As for the "security" of a buzzer door, it's a layer of security in the overall "blanket" effect. Nearly any door can be breached with enough time/effort/tools. This is about adding a deterrent; a barrier. It is in no way entry-proof; it's entry resistent. It's yet one more thing that can delay or deter someone from gaining entry effortlessly. Don't think of the buzzer door as a 12" thick bank-vault door, but it certainly is something that will deter or delay some (but not all) undesirable people from coming in. Someone who, in the heat of the moment, decides they want to walk in and use the restroom is gonig to be deterred if the appropriate system is in place. Conversely, someone who's Hades-bent to gain entry and brings tools (sledge hammer to defeat the door jamb or firearm to shoot through the door glass) is very likely to gain entry because the door itself is easily defeated when the right tools and effort are present.
The question is how the business decides to balance the asthetics of the building versus the need for security. Metal doors are better than glass doors, but don't look as professional at a doctor/dentist office. Buzzer systems improve access denial, but are an admission that the surrounding area is risky. (I'll note that anyone who uses that business and lives in the area is already aware of the sketchy area in the first place).