That depends what tree you have and what you are trying to achieve. Obviously if you have satsuki azalea, you probably want to leave the flowers on the tree! If you have a crabapple, personally I don’t think there is much point if you don’t let a few fruit form. And I am really partial to rose-coloured larch cones. All trees form some kind of reproductive organs, whether they be conifers with their strobili (cones, either pollen or seed forming), ginkgo with their ovules, or angiosperms with their flowers and fruit. Some are almost unnoticeable and others are right in your face. Bonsai wisdom sometimes says these should be culled or removed entirely in order to avoid draining the tree of its energy.
When considering this question we need to understand the idea of resource ‘sources’ and ‘sinks’ in plants. A source is a material producer and exporter, and a sink is a material importer and consumer.ref See the below table for sources and sinks in trees. As you’d imagine, leaves are a major source of carbon and a sink of inorganic nitrogen (nitrogen as a macronutrient). Roots are a source of inorganic nitrogen and leaves are a sink. So what about fruit, seeds, and flowers, which supposedly drain the tree? As you can see they are major sink organs – but not only sink organs…they are also source organs!
Let’s have an interesting little diversion – did you know that it’s not only leaves which photosynthesise? This fascinating studyref looked at the photosynthetic activity of (a) ears of wheat (b) sycamore seed pods (c) a green tomato (d) unripe and ripe strawberries (e) a greengage (f) unripe cherries; and (g) a green apple. The images below were taken using fluorescence imaging and anything with a colour indicates that there is photosynthesis taking place – with the red and orange areas the strongest. Check out the sycamore seed pods!
How the heck can this happen – well there are various theories about the mechanism (including recycling CO2 from respiration, and the presence of stomata on fruit) but the point is that maybe seeds and fruit, particularly if they have periods when they are green, don’t act as such as sink as we might think, and for a period are acting as a source and not a sink.
This study states that “reproduction in Beech does not deplete stored carbohydrates, but it does change the amount of nitrogen stored” and this study found that “fruiting is independent from old carbon reserves in masting trees”ref which basically means that fruit uses current year photosynthates/energy and doesn’t actually deplete reserves.
On the other hand this study found that Douglas fir tree rings were narrower in years when they bore many seed-conesref and this one mentions that “experiments with apple trees have shown that roots can die from lack of carbohydrate supply when they are over cropped”ref
All living things have processes for managing and balancing resource allocationref and this is likely an evolutionary differentiator. In trees, resource availability limits the amount of fruit which is allowed to develop – even pollinated flowers may not develop into fruit if the tree does not have enough resources available – these could include energy, or nutrients.ref So to an extent the plant itself manages the resource allocation.
To complicate matters further many trees use a ‘masting’ strategy for reproduction, which means they have years where many more seeds are produced, often synchronised with other trees of the same species. One theory for how this happens is that the weather influences how pollen is distributed – in beech windy conditions lead to mast years whereas in oak short pollen seasons do.ref Temperature and precipitation also affect pollen production and distribution (high temperature increases pollen production but high precipitation washes it away).ref In this study on Japanese oak, “high seed production never occurred in two successive years, but successive years of low abundance were observed several times between 1980 and 2000.”ref
Overall there are a lot of factors interacting when it comes to reproduction. Photosynthetic seeds or fruit can contribute to carbon production, and may use only current year photosynthates, so the tax may not be as high as thought, but there is some evidence that reproduction can divert energy from roots and foliage.
If you are really focused on trunk growth, branch structure or foliage development on your bonsai tree, you might want to divert the energy from reproduction to these areas by removing some or all reproductive organs, until you are happy with the trunk/foliage. At this point then you could then let the tree reproduce (noting that removing cones one year will cause more cones to develop the following year)ref.