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One problem with not trimming is that the nutrients will be going to all of the branches and leaves that are below the flowers and fruit instead of going to the fruit to grow. The optimal way for fruit production is to keep the tomato growing as one single stem trimming away all the branches and suckers below your first flower growth.
I let the hydroponic system grow free but here are pics of my other tomato plants that are training to be trees

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Aww man. Trimming seems like I was hurting the plant. I should look at it like a hair cut. Lol
Thanks. Needed this info.
Have a wonderful weekend!
Joy

Start with the dying or discolored leaves at the bottom! Thank you for coming by.

Ok. Will do. Thanks. ;)
Joy