Leaving your deck joists exposed to the weather will rot them out much faster than if they were protected. Here is an example of the top joist of a 2x12 rotting from being moist all of the time. Only a half inch of the entire 2x12 was destroyed so no need to rip the entire joist out. The joists were strengthened with extra pressure treated wood near the top where moisture sits. This way when deck boards are laid they are flat to the touch via the new board. Then we wrapped with either commercial grade garbage bag plastic and/or roof tar paper. You can also paint the wood with a weather proof membrane, but I find thick plastics and tar paper the are best protection.
There is always this stuff as well: https://www.amazon.com/TimberTech-PRO-Tac-Flashing-Joist-Tape/dp/B07VQPTB37
But for $90, Iām sure you can find an alternative
Remember if the under side of the deck is exposed you must think about aesthetics to what the repair will look like. In this case it does not matter as the bottom is getting covered with under decking. Cheers!