Before I begin the discussion about dividing plants, let’s talk about this lovely plant. It’s one that I have had, most likely for about 8 years or so. I just got a smaller identical one (labeled foliage plant, of course), and then one with slightly different colors labeled as a calathea.
This plant is one that I have always known as stromanthe tricolor. I have also seen it as stromanthe triostar. But I have never seen it called a calathea, despite the fact that its leaves do move in relationship to light.
But I had my other calathea/stromanthe with me at my most recent house plant lectures, as well as 2 aglaeonema. I got asked about dividing plants at each lecture.
Both times my answer was the same: generally, I don’t divide plants. I like my plants to look full. Certainly there’s no reason not to, particularly if there are multiple plants in a container.
But this brings me to a different issue. When you have had a plant for several years, and you have re-potted it a few times, you probably want to “renovate” it.
What do I mean by that? I mean that you want to carefully groom the plant (usually this can be done without taking it out of its pot), removing old stems, and even old dead plant parts if you find them. I did that with this stromanthe before I took the above photo.
This is the crud that I pulled out of it. Notice all the dead stems.
There was even this little bit of dead plant stem in there.
By the way, all of this is on a glass-topped table. The signed poster underneath is from several years ago when Allen Smith came to Hartford for our Hort. Society. I was lucky enough to be one of the ones to be selected to record a radio show with him and he gave us all posters as souvenirs.
So, if you choose not to divide your plants–as I do–it’s just fine. Just be sure to renovate them every so often. They will thank you!
Gardendaze 
They all have different personalities. Some may not need renovation for a very long time. Since I like large Ficus benjamina, I let mine grow, and merely prune them around the nearby furnishings, and then put them in larger pots only very rarely. However, Canna (even if grown as houseplants) get divided almost too regularly just because of how they grow, . . . and because I enjoy dividing them. They get cut back and put outside for the winter, so renovation is at least annual.
I was reading your post today about all those summer corms and tubers that get so large that they take over. I have to tell you that only in extremely rare instances do they do that here–and that would be of the ones that “might” survive our winters. Nothing is going to survive the minus 9 we just had last weekend with no snow cover. We’ll get crocosmia to winter over every so often–and then we have a winter like this one and that’s that. So yes, you’re right about plants and their “personalities” and needs. I should have shown the snake plant that broke right out of its container because I was too lax in my re-potting. Oops.
Writing for two different regions can be awkard for that same reason. Perennials that are aggressive and weedy in Southern California are not so aggressive here, and some are sensitive to the very mild frost here. It does not get very cold at all here, but some tropical plants are very sensitive to even the mildest of frost.