Agapanthus aside for a moment - maybe it is that some plants have adapted to prefer constrained roots - if you think of somewhere like a forest floor or other heavily populated tree or plant based area, it may be that that is so congested with other roots that they have adapted to cope in that environment? Maybe - I'm no Darwin!
I think it has more to do with stressing the plant to force it to produce more flowers. If for example an Agapanthus has loads of room for its roots, it will produce lots of leaves as it's the leaves that provide energy for the plant. It almost certainly will flower, but not as much as if its roots are constrained. When the roots are constrained, the plant fears it may be dying, so puts more energy into producing flowers to ensure the continuation of the species. But so long as it's given enough water and nutrients, it won't die. It's a bit of a cruel trick really
Billericay - Essex
Knowledge is knowing that a tomato is a fruit. Wisdom is not putting it in a fruit salad.
I've seen this mentioned in many articles on houseplants - for some, being pot bound can trigger a survival strategy to produce flowers or offsets as the plant senses that water and nutrients are limited. This article makes interesting reading: When Is It Time Repot A Houseplant (gardeningknowhow.com). Sometimes feeding can encourage more leafy growth as the plant thinks there's no need to waste energy on producing flowers and offsets.
That was my point earlier @Batesadrian - there's huge differences between a plant naturally occurring and one we deliberately grow.
As @Pete.8 describes, stressing a plant is often a way of promoting flowering - tomatoes are a prime example. If you don't have flowers you don't have fruit. Annuals in particular, are striving to complete their life cycle, and the stress of thinking they're going to die triggers that action. If you're too kind to them, they get too comfy.
Of course, that doesn't always happen. Excess food can help create more flowering in certain plants.
It's a place where beautiful isn't enough of a word....
I live in west central Scotland - not where that photo is...
Also agree with @Pete.8 When we say a plant 'likes' to have its roots constrained, it's a bit misleading - the plant doesn't 'like' it at all, but we may like how it makes the plant grow.
"What is hateful to you, do not do to your neighbour".
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If for example an Agapanthus has loads of room for its roots, it will produce lots of leaves as it's the leaves that provide energy for the plant. It almost certainly will flower, but not as much as if its roots are constrained.
When the roots are constrained, the plant fears it may be dying, so puts more energy into producing flowers to ensure the continuation of the species.
But so long as it's given enough water and nutrients, it won't die.
It's a bit of a cruel trick really
Billericay - Essex
Knowledge is knowing that a tomato is a fruit.
Wisdom is not putting it in a fruit salad.
The video on this GW link states that restricting roots and feeding are important for potted Agapanthus: How to Grow Agapanthus (African Lily) - BBC Gardeners World Magazine. Looks like you've done the right thing @Uff !
As @Pete.8 describes, stressing a plant is often a way of promoting flowering - tomatoes are a prime example. If you don't have flowers you don't have fruit. Annuals in particular, are striving to complete their life cycle, and the stress of thinking they're going to die triggers that action. If you're too kind to them, they get too comfy.
Of course, that doesn't always happen. Excess food can help create more flowering in certain plants.
I live in west central Scotland - not where that photo is...