It's not a tree, it's a naturally suckering shrub. It's perfectly healthy. You can take out older stems periodically to rejuvenate the plant.

It is important to remember that one of the primary features of this shrub is its layered, heavily tiered growth habit. One of the reasons it is sometimes referred to as the "wedding cake" shrub. Those layers are what shows off those upward rows of paired flowers that make it such a spectacular springtime show. For that reason, I would certainly thin out a majority of those straight, vertically growing suckers, leaving just a few (3?, 5?) of the largest to increase height and fullness.

What you have now is simply too congested.