If it's that easy why doesn't it happen all the time? People who fly just have more integrity? It's an honor system in the sense you can grab any bag you want sure, but they have all your info bro. Not to mention tons of security and cameras everywhere.
You give them your personal info when you buy a flight, they put a tag linked to your boarding pass. The airline and airport knows who the bag belongs to where that person is going along with their contact info. If someone can't find the bag, they'll tell airline and the authorities, who have your passport/ID, phone, email, sometimes address. Unless you planned this from the beginning and used fake info and covered your tracks once you leave the airport. If you drive your own car or get a taxi, they'll easily track down the license plate. You should use public transportation and make multiple transits and use routes with no cameras.
You should just try it next time and see how far you get away with taking someone else's bag.