Several years ago, a Tektronix sales engineer came into my office hoping to sell me their latest $30,000 TDS784 digital scope. I listened to his sales pitch, and then pulled from my pocket a small device powered by a 9V battery and said, "show me the signal on this output pin." For about fifteen minutes he pushed buttons and turned knobs, struggled with aliasing and uncertain trigger level, but he couldn't get a sensible display. I powered-up my trusty old Tek 465B analog scope, and in a few seconds we saw the sinewave+pulse waveform clear as day. The 9V powered device was an old oscilloscope demo board made by Tektronix!
If you know exactly what you want to measure, digital scopes are great. But if you are just poking around a circuit ... well ... I did not buy that fancy new $30,000 digital scope. Even today, I still use analog scopes most of the time.
You can get a halfway decent used analog scope for $100.