And thus we get into the arbitrary nature of fare structures and how they could be changed to anything at all provided the overall income was the same, I guess. In essence, that means that the above point isn't quite right.
Looking at the bus-only tickets, a significant number of people (probably the vast majority) are making a simple return journey. Thus, most people buy the £5 ticket. A few people aren't, either because they are changing to another operator along the way, or because their tendered evening service (remember those?

) is a different operator. So let's say it's 9/10 people pay £5 and 1/10 pay £6.
The outcome of that is that if you abolish the £5 ticket, you can reduce the £6 ticket (which everyone now buys) to a considerably lower price. Using the above (out of a hat) numbers, and assuming that such a small increase wouldn't really affect demand, your "any bus" ticket would actually only need to increase to £5.10.
But that's probably an oversimplification. Day tickets covering entire major cities are a bit of a blunt instrument. Enthusiasts love them as they can ride round in circles all day, but there are other models possible which allow one to pay less if travelling a shorter distance - zonal tickets being a key one. So instead of you paying £10 for a ticket that you can use to take a bus to Glossop station, then a train to Manchester, then another train to Wigan, then a bus to your Nan's house, when all you're doing is going from Levenshulme to Manchester, say, then you would instead buy a "zone 1-2" single or day ticket which would allow you to make that trip by any mode or combination thereof as you wish. That's how all the Germanic systems work. You
can buy a ticket for the entire (Hamburg) HVV-Gesamtbereich, for instance (covering an area not dissimilar to a 1-9+Watford Jn Travelcard, say) but I suspect almost nobody actually does on a frequent basis.
There are multiple zonal models (e.g. concentric and cell-like), and even the UK has some, e.g. Merseyside and London being two different ones (the former having a "cell like" system rather like the German and Swiss ones, the latter having a purely concentric one).
I completely agree with all of those, noting as I usually do that anyone who designs bus lanes in the UK seriously needs whacking round the head with a German or Dutch design manual for such things - plus we need legislation permitting the use of tram signals for buses, which makes junction "overtakes" not need an island and thus be possible in far tighter spaces. Having had experience of living in both Germany and the Netherlands (Switzerland doesn't really count in my experience as I've not lived anywhere there busy enough to really need bus lanes), and seeing what arrangements they have, ours are just a useless joke, often petering out before junctions for the bus to have to push in, and not designed with specific routes in mind (e.g. an overtake from the left to turn right), nor do they give the bus absolute priority - and stop locations also don't help, as putting them by the junctions makes use of any necessary wait.
Edit: And let's add the bus operators' own doing - the need to negotiate a financial transaction on boarding, which is
still the case even with widespread contactless payment. So these zonal tickets should be on sale in newsagents, Tesco Express etc, so the bus driver doesn't need to sell them. More people need to have season tickets by adding good value options for off-peak use like the "CC-Karten" common in Germany. And we need tap-on, tap-off contactless with capping with urgency. That buses often have to stop for 30 seconds to a minute every 200 yards is costing operators a fortune and a major cause of bunching and increased PVR and thus costs. Vehicles and payment mechanisms need to be designed for a typical stop to be 5-10 seconds, and for loading a full sized single decker to full and standing maybe a minute at most.
But why does it matter? Because what we never look at, for some reason, is why those people who
aren't using public transport don't use it. And very often, you'll get things back like "too expensive" and "too slow" when it comes to journeys that aren't a direct trip into the city centre. And the cause of that is poor connections and financially penalising people for having to change bus. That's a mindset thing. A two-operator ticket is not a premium product commanding a higher price. What it is is a financial penalty for having an awkward journey. I completely get the idea of further costing more, either zonally or on a per-mile basis, and so can most people, but the idea that arbitrarily requiring two vehicles, either by one or two operators, for your journey should cost more is just bizarre. London has taken how-many years to get that, but it finally has got it - how long for everyone else to get it?