Licenses with every BON? The cost and administration would be prohibitive and it is not possible to work in more than say 4 states a year if you are doing 13 week contracts. Every state has a different time frame for licensure, from "walk-through" to the hassle of having to verify every license ever held, or as you are discovering with Florida, prerequisite CEUs and background checks.
Every traveler has a comfort zone in how they handle renewals or proactively getting licenses ahead of travel offers to be more marketable. Many states have very easy renewal of lapsed or expired licenses so I just let them lapse unless I know I will be traveling there soon. Lapsed fees are fairly trivial in most states (NJ being a huge exception). About half of the states are in a compact agreement whereby if you live in one of those states, you can legally work in the other member states without a new license.