The only reason for cutting the upper limbs of a crape myrtle is to remove limbs that cross or to reshape trees that were planted in too tight a space. Lower limbs may be removed to form trees which is my preference. Crape myrtles in a tight space could be cut to the ground every year and grown as a shrub.
Better would be to buy a dwarf form to fit the space.
Lilacina Crape Myrtles in my front garden.
Pink Crape Myrtle planted where it has room to grow,
the first consideration in choosing a tree.
They come in colors from White to Purple and all shades of red and pink.
Rarely do you see mention of fragrance. I've only noticed fragrance in the white.
Crape myrtles provide fall color,.
The colorful crape above is shown from the opposite direction in the pic below from the previous year. As Crape Myrtles grow, the lower limbs are pruned to show the sculptural forms of the trunk and reveal the exfoliating bark.
I put Crape Myrtles at the ends of groups of 3 Loropetalum.
When Crape Myrtles are to grow as trees, from 1-7 trunks are left. There are specific instructions on many sites online on pruning for best form and how to recover a tree that has been pollarded leaving ugly knobs. The best information comes from University Extension sites. A landscape care business that I looked at said that the knuckles left when trees are topped over and over provide 'energy for new growth.' I don't think so.
My opinion is that cutting off the tops down to nubs causes the tree to expend energy from the roots to grow new branches before it can put on blooms.
Natchez, never murdered.
In the summer when the first flush of bloom fades, I deadhead as high as I can reach for better rebloom. Cutting the old bloom heads and pruning away any suckering at the bottom is all the pruning necessary.
Joining the flower fest at Tootsie's Flaunt Your Flowers.