In the 80s, your VCR would frequently be plugged in, and it would keep pumping out a placeholder blue screen at a minimum, particularly if connected via antenna

In the 80s, your VCR would frequently be plugged in, and it would keep pumping out a placeholder blue screen at a minimum, particularly if connected via antenna passthrough. However startup time would be minimal - a couple of seconds - compared to warmup for the CRT, which would usually be at least 10 seconds before it would look settled. But I recall devices generally being much faster to start up. A C64 would boot to READY prompt in 3 seconds. The penalty for turning off completely and needing to wait for boot was small, and for computing devices, wait time was dominated by loading, not booting. You might have to wait for a rewind with a VCR, and you'd certainly wait for tape loading on devices in the C64 class. Consoles with cartridges didn't take long to boot up and load though.