You are still responsible for tracking the aircraft operating time for maintenance purposes. If you have neither a Hobbs nor a recording tach, you would have to keep a log of all flight time on the aircraft for that purpose. However, I suspect that while there is no reg requiring all planes to have recording tachs, those without some other device are probably all manufactured and certified with a recording tach, the removal of which would be an alteration requiring FAA approval, one condition of which would likely be the installation of some other flight hour recording system like a Hobbs meter. I know for example that the Grumman GA-7 Cougar came from the factory with non-recording electric tachs, but there is a factory-installed Hobbs meter wired to the weight-on-wheels switch to record flight time for mainenance purposes.
BTW, most flight schools and FBO's are aware of this not-exactly-new trick, and have their Hobbs meters wired straight to the battery through an oil pressure sensor switch rather than through the electrical master.