I very frequently use single shot to capture things like startup and transient response of power supplies. I also frequently capture and save waveforms for later comparison. It's also not uncommon that I want to look at the analog aspect of a digital signal.
Exactly this, and much more. Power sequencing, RC circuits...
Problems with three-stating, pull-up values, speed, interference... Analog levels like current measurements, comparator setpoints. Whatever. Most control aspects in modern electronics are non-repetitive, or irregularly repeating (i.e., not constant frequency) events, and can't be sampled as binary signals either, or doing that loses too much information. So both analog scope and logic analyser are out, often.
Logic analyser is more optimal, possibly fast to use, for some large datasets, but if you go the recommended-by-some "buy an analog scope and a cheap logic analyser" way, you very likely find out you need to
still buy a DSO.
A beginner usually does not have unlimited budget and bench space.
A modern low-cost DSO can alone and completely replace these three instruments (DSO, analog scope, logic analyser) no problem whatsoever, and to a limited but often quite sufficient extent, also a spectrum analyser. I do exactly that, all the time, both professionally and for hobby, no problem. If I required very large amounts of bus decoding, a logic analyser would be a timesaver, making life a bit easier. A process optimization, really. I can see no use for analog scope at all, it would be "just for fun".
You can buy a massive set of different kitchen knives and lie to yourself that now you have "right tool for every job" but as every professional chef and kitchen enthusiast know, a good universal kitchen knife that is kept sharp does most of the jobs and all those specialized ones see no use.
I have had all three instruments mentioned at my disposal and I always end up working with the DSO alone.