You can still play if you don't upgrade. You only run into an issue with new titles that require a higher firmware. But considering new firmwares can add new features like the ability to boost the CPU clock during loading you also can't reasonably expect them to ensure every game works on every firmware.
If you already have a game and it runs today on the current firmware you can at least keep playing it offline by just skipping the system or game update.
New games and game updates often require Switch system updates. Two examples:
Animal Crossing DLC requires a system update.
Rocket League seasons usually require a game update.