I tried the approach of asking myself "if DRT is the answer, what is the question". I struggled to find an answer.
DRT is only conceivably good for travel that has high social need. Given the state of public finances, low-to-medium social need isn't going to be enough to justify hefty subsidy.
But DRT is only actually good for travel that has a high tolerance of uncertainty - until a few days or hours beforehand - about whether you will get a ride at the time you wanted, at a different time, or not at all.
Nearly all the major categories of high-social-need transport fail the tolerance-of-uncertainty test. Getting to a job? - you'd be lucky to last a fortnight when each journey request has only about an 80% chance of being met. An outpatient appointment? - good luck when you asking the appointments team to let you come back to them with your preferred time a week ahead of the appointment. Getting to an interview, an exam? Onward travel by train, bus or air where affordability requires you to fix your time several weeks ahead? Forget it.
Shopping is the one application where there is perhaps a reasonable level of tolerance of uncertainty. If someone can't get to the shops on Tuesday morning, then there is a fair chance that they might cope with going on Wednesday afternoon. But the widespread availability of online shopping substantially shrinks the ranks of those for whom travelling to a shop is the only way of keeping fed.
I could only think of one high-need category of use where most non-car-users would find DRT a solution - clothes shopping. What have I missed?
Many DRT systems do allow relatively long term booking and repeat booking functions so to a limited extent they do get used for employment/education movements and these trips are the most likely to have multiple booking as they are all likely to be heading to a similar area at a similar time. We run some DRTs where there is an issue getting a booking before 0900 now because of regular travellers having the vehicle booked up.
In terms of high social need reasons for supporting these services getting the isolated elderly and poor to their nearest shop for food shopping is actually quite important, they are the least comfortable with online purchasing (all the DRTs we do offer a phone line booking option even if they push the app for just these people), there are people who still do not have access to payment methods that would allow online purchasing and getting to the shops also has an important mental & physical health role for these groups as well so don't dismiss that group of off peak travellers.
In rural areas there is a benefit in DRT in allowing a service to be provided to more settlements with the same effective resource (we have a DRT route requiring 1 bus which replaced a 1 PVR scheduled service but twice as many villages are included in the area) but it relies on the booking and scheduling system working better than they currently do, I get a feeling from seeing reports that they still aren't quite flexible enough to adjust journeys (particularly when people are booking, rather than just saying nothing available actually offering times when it is) to get the best out of the concept. It is a very specific solution to a very specific problem, mostly rural, and will never be commercial as a bus but it does hit a need. The buses used tend to be slightly bigger than demand generally needs but low-floor vehicles are preferred for accessibility purposes (and avoiding the need to fit/maintain lifts) and operators favour the slightly larger Sprinters for their reliability over slightly smaller but less robust models from other suppliers.
A good DRT scheme should be examined to see if clear demand patterns to see if there are enough people travelling on specific flows or at specific times to possibly put together regular scheduled trips to serve those flows which may allow new passengers to be attracted whilst providing extra certainty for those established flows. Whether anyone is thinking about this, the DRT proponents probably aren't going to push that as it doesn't suit their agenda, and whether any of the latest collection of schemes will last long enough to do it in this manner (as opposed to replacing it at the end as the funding runs out) is a clear question.