To be fair, trains are already heavily used for domestic tourism, in addition to personal or business travel. Most biggish towns are well connected by local trains, and big cities in the north and center are easy to reach with the high-speed lines. For example, the popular Cinque Terre destination in Liguria is well-connected by a train route that touches all five towns with a frequent schedule, every 20 minutes or so. If you don't need to move too much at your destination, a train is often the most convenient way of reaching it.
Something I often use is the bicycle transport on local trains, allowed with a very low fee, like 3 euros: starting from home, follow any scenic route that ends in a town with a train station, and use the train to go back home. Bonus points if the route touches multiple towns, so if you are too tired after 4h on the bike, you can cut it short and go back anyway.