To be fair...
At a very minimum along with the swipe of a SIDA is the requirement of the use of a 5 (or more) digit pin code - usually on a scrambled pad. A badge alone would NOT grant access through a secure portal. The only other way to a sterile area within an airport is through a TSA checkpoint - which requires a visual match by a TSA officer of the badge to the individual accessing the checkpoint.
You are correct. I work at an airport, and part of my job is monitoring who goes through what doors. Also, the badges are audited by the TSA. If you lose your badge, there is a large fee in order to get it replaced. That is because, if during the audit, it is discovered that more than 10% of the badges are lost, then all badged personal must be re-badged, and no airport wants to go through that! (10 years ago we replaced our security system and we had to rebadge 3000 people, and I work for a small airport!) For instance, at my airport, if you can't locate your lost badge, you must pay $100 to replace it. Airports that have badges with Customs clearance charge upwards of $1000+ to replace it. And, just because you have a pin number, it does not mean you have access to every door. The doors are assigned to your work area only. If you try to open a door you do not have access to, I will dispatch a leo to check you out. Some badges have no access assigned to them. They are just for identification purposes only, ie rental car agents, food workers on the non secure side, etc. Badges are of different colors too, to indicate where they are allowed to go. For instance, at my airport, anyone with a white badge can't even go through security. They have no reason to go on the secure side. If an employee has forgotten their pin code, they must come see me in person and I check identification before I give them the number. (It happens with contractors who are not at the airport often, but are badged.)
Also, as soon as a badge is reported lost, it is disabled in the system so it can't be used by anyone, even if you know the pin number. It immediately alarms me to send a leo if someone is trying to use it. It is to our advantage too, as if someone does set off an alarm and does not immediately contact us (accidents happen) I will shut it off until they contact me.