I know what you mean - I remember finding that same issue when we toured the low lands, and when riding rail trails in Oz.
It seems like a great idea having a nice cruise on modest gradients, but after a while your legs start begging for some variety. 
I was thinking about this as we rode up a long climb in Japan today.
Standing to climb when riding a bike loaded up with panniers is a bit more challenging than on an unladen bike.
Touring with a weaker rider has its own challenges, when we are aiming to remain in sight of eachother.
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“I live in a flat part of the UK…”
^ I didn’t know there was one! Certainly not anywhere I’ve been in the west, north or southeast where 20+% is depressingly common.. Norfolk maybe?
I’m from England so a slightly different category of climbing than a lot of posts here. Although I have ridden in France, and I enjoy climbing for the same reasons there too. I often measure the success of a route by how many ‘Unsuitable for HGVs’ signs I pass as I explore random lanes around the south east. Which means the climbing is shorter but nearly always unexpected, there’s no real indication where your climb stops, whether the short rise is just that, or just a precursor to a longer climb, whether this dip means we’re near the top or the climb continues to rise out of sight ahead
You fly down a dip and power up a quick rise only to realise that this is nowhere near the top
Or you modulate your effort to cater for steeper pinch only to find you’re heading back down again straight away
Somehow experiences on the climbs stay with you:
One of my favourite moments comes from cresting the top of a, this time fairly familiar, single track lane. Turning - out of breath - into a flood of early morning sunlight glistening and glostening through the trees, serenaded by the dawn chorus as I get my breath back and mentally prepare for the next kick
Or arriving above the tree line at Ventoux, seeing the view for the first time and realising this is why you’re here, and that you have such an uncontrollable grin on your face
No amount of flat gives these enduring experiences
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Ha, no, but Bicester north of Oxford (and only known for a designer outlet). I can get into the Chilterns, Cotswolds etc on a ride to get some climbing in, but most Hill Climb events are a 2hr drive away in any direction.
Luckily I met my partner through cycling so we have a common passion, I’m very fortunate to be able to spend our vacations seeking out cool riding in big mountains (we even raced Haute Route Ventoux in the pairs category 
).
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Climbing Arquette d’Ancizan in the Pyrenees, the tunnel of trees stops lining the road just as you crest and burst out into an absolutely picture perfect valley that fills your whole field of view. Despite being over threshold (this was another Haute Route event) it gave me goosebumps.
Didn’t truly know what climbing was till I moved to Colorado. There, everything you described in your list applied. 
Regarding gearing, I installed lower gearing as it allowed me to comfortably match the slower pace of my friends. I feel there can be lots of camaraderie in cycling and I love a good social ride.
Keep climbing, my friend!!
I live in Colorado and am a mountain biker. I love to climb which is fortunate as you have to climb steep to enjoy the ride back down. I may not enjoy it in the actual moment but for sure it is a big part of the enjoyment of the ride. I love the focus and challenge. It’s why I do not love road cycling at least as much- why be around cars, flat pavement with no technical challenges (needing to adjust the bike and body position for traction and clearing features) and just pure power application. Ironically, one would think I would like that best as a former long time competitive heavyweight rower and sculler. And my mountain bike gearing is a 30 or 32 chain ring and a 10-52 cassette.
I’ve never been a great climber, now with age and some weight I keep getting worse. Still I enjoy it. Cycling is my meditation and never more so than while climbing. It’s easy to be distracted by speed, distance, power…but on a long climb there’s nothing but “keep going”.
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A lot of it just comes down to whether people enjoy the sensations of slow bikes versus fast bikes I think. Most cyclists seem to enjoy riding in the “fast” regime by default, as the bike tends to be stabler and more forgiving.
Even when gearing is low and fitness is high, there comes a point as the road steepness where speeds fall and the sensations change. This is where Climbing begins, and even if that happens at a different gradient for you than it does for me, that point exists for everyone. At these speeds, the dead spot becomes noticeable each pedal stroke, the bike gets twitchy, you have to negotiate with the road texture, and every little acceleration, falter of power, or pitch change in the road can demand a gearshift or push you out of your ideal cadence range. It’s a much more active experience that demands more attentiveness and interaction from the rider. If you don’t want to engage with the bikeriding of it all, climbing feels punishing and annoying, but choosing to lean in to the experience makes riding feel more interesting.
I currently live in a 150 foot-per-mile kind of place, but I’ve previously lived and ridden thousands of miles in a miles-per-foot place. I’ve learned to love both climbing and riding on the flats but they are very different experiences for me. Climbing makes the bikeriding much more engaging but it also demands that attention, sometimes to the detriment of other aims I might have for an outing. Flats let me focus on something else, whether that’s exercise, introspection, socializing, or just listening to a podcast.
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Love climbing, 7-13 miles 2-4000’ (3-6000m?) up fire road or non-chunky single-track, a mental battle for the physical & review of the self dialog, then the rip downhill, southern California terrain so dry & sketchy, old person perspective
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