But when it comes to a problem on the motherboard, the scope is IMO more than useful, just to check clocks and some other signals like the video output, activity on busses etc....
For some problems, the logic analyzer is also needed. As an example, I've got a failing CPC and I didn't want to change blindly chips:- With the scope, I detected that the synchro signal was not generated by the CRTC. Without a scope, you can't see this
My logic probe has a "pulse mode". With that you can check if the output / chip is alive and generating a non-steady signal. I used that mode to check RAM chips (chip select, RAS, CAS, inputs, output).
A logic probe is onle 30 €, whereas a scope that can be used for Mhz digital signals is a couple of hundred €, even the cheap ones (there are little DSO pocket scopes for about 100 $, but they are toys and don't have the bandwith for digital signals, they are only useful for audio / analog really)
I am not saying that a scope and/or logical analyzer is not useful. But I would not advise people to get one if 99 % of the situations (including some of the ones that you have just described) can be analyzed perfectly fine with a logic probe.
And from a time management point of view, before you have figured out how to hook up and read and understand the databus and CRTC signals, you would have already replaced the CRTC with a fresh one. The good thing about the CPC is that it only has a couple of big chips... in principle, I am not a fan of blind repairs, but for the CPC it is possible. Buying a new CRTC is not only more cost efficient than buying an oscilloscope or logic analyzer, but also much more time efficient.
All this is of course only advice for people who are not electronic geeks and don't already have an oscilloscope and logic analyzer. So I would not suggest to people to buy such equipment in order only to repair a CPC (unless they want that equipment anyway of course).
Just my few cents.