Do single company tickets improve overall public transport patronage?
If you're going to pose a question like that, it also needs to have a suitable measuring metric. How would you determine specifically whether a customer is taking public transport because of the availability of a specific ticket, rather than because they generally need to? I could just as easily ask you to prove that multi-operator day tickets improve patronage.
You are wedded to the idea that only multi-company tickets should be available, because it's what "people" want (without any evidence to back up your statements, let alone from non-bus-users). By extension, that would appear to prohibit operators from offering anything else - be that a single company day ticket, a route-specific weekly over a major flow or any special offer (such as a reduced price evening fare). How would this benefit, say, a situation where two companies operate over a route during the day, but only one provides early morning and late evening journeys when our hypothetical traveller only has one option, thus has no need for a hypothetical multi-operator ticket?
What about areas where almost all services are provided by a major operator, and only a few tendered services are run by another company? Will the majority of passengers need a multi-operator ticket?
Would you expect to be able to use your Tesco Clubcard points in the neighbouring Sainsbury's because they are all providing a "supermarket service"?
Oxford may be good bus territory, but that is largely because of the operators, not necessarily the councils, who have made life increasingly difficult for operators to serve central Oxford. The current timetables, worked out under a quality partnership, were already designed to reduce the number of buses in central Oxford, and were shortly thereafter followed by an abdication of any public transport publishing by the County and City Councils (The County Council's "journey planning" link takes you to Google maps) and an axing of all, or almost all, subsidy for tendered services; hence the large number of 'community' operations almost invisible to the visiting public.
Fundamentally, though, ticketing is a very minor element of these changes. The greater elements are the withdrawal from certain corridors of long-standing operators, and particularly the withdrawal of Whites Coaches from the Didcot town services. This small operator has gradually stepped back from provision over the years, and these are its last regular (It appears to retain a public school service, the 145C, and private contracts) public services - using a yellow vehicle, last time I saw them, admittedly some years ago!