I have used 2-channel and 4-channel scopes, and I can't recall a time when the extra channels made the difference between possible and impossible. But I can recall many times they made the difference between easy and hard.
One example: I was using a ham radio transceiver with an external amplifier, transmitting Morse code. The output was changing in amplitude suddenly. (to reduce bandwidth, good Morse code transmitters avoid instantaneous on/off transitions, taking a few milliseconds to ramp the amplitude up or down.)
To diagnose the problem, I had to look at the RF input to the amplifier, the RF output, and the line between the transceiver and amp which tells the amp when to switch between transmit and receive mode.
At the time, I only had a 2-channel scope. A 4-channel unit would have cut the diagnosis time to a fraction of what I needed with that 2-channel, because 2 channels forced me to go back and forth several times between the various signals to see the relationships.
It turns out there was a firmware issue with the amplifier, where it would switch on amplification late, but only if it had recently been switched off. A string of rapid-fire Morse dits would attempt to toggle the amp on and off too fast.
I emailed the amp designer a description of the problem, with screen captures from the scope, and less than 24 hours later, he sent me updated firmware that fixed the problem!
Details here:
https://ag6qr.net/Radio/HR50Clicks/