I would argue that you can be spontaneous, with the caveat that you might not be able to get FP+ for specific rides. You can change your FP+ at any time in the WDW app, and I'm among those who have had great success scoring good FP+ on the day I'm there. Going solo gives you a particular advantage at that, too, since it's easier to find last minute FP+ for just one person.
I'm not sure if you're aware, but once you've used the three FP+ you reserved ahead of time you can make more FP+ reservations for that same day in the app. You can also adjust your existing FP+ reservations on the fly. You might see people on this board talking about "the refresh method"--what they mean is that you go into the FP+ menu in the app and just click back and forth between different time slots to refresh/reload the options until the FP+ you want pops up. Then you reserve it, even if it's for much later in the day than you want, since it's faster to refresh the "modify FP+" menu than to keep trying to book a new one from scratch. Just refresh the app until you either get what you want or decide you're sick of trying. It works surprisingly well; I was able to get somewhere around a dozen FP+ in one day, including several headliners.
That being said, if you have already reserved a FP+ for a highly sought after ride (Flight of Passage, Slinky Dog Dash, 7 Dwarves Mine Train, etc.) and you have your heart set on riding that ride and being able to use a FP+ for it, it's better to keep what you've got. There's no guarantee you'll be able to get a FP+ for those high-demand rides day-of. A bird in the hand is worth two in the bush, etc., etc.