To what kind of Jesse tree are you referring?
I ask because some people use the phrase ‘Jesse Tree’ to refer to what I prefer to see called an “Angel Tag tree” or a ‘Gift tree’.
A proper Advent Jesse tree will have (mostly) barren branches which will be decorated with ornaments that refer to ancestors of Christ and/or symbols of scriptural prophecies about the coming of Christ.
Of course there are also stained glass or tapestry depictions of Jesse trees.
The problem I see with Jesse trees is that they often look very amateurish and so not all that worthy of being inside of a Church. The ornaments need some sort of explanation which doesn’t really fit any liturgical context. At least in the United States, it is no longer that common for children (or adults) to get to go to daily Mass so they would not be getting the sense of time progression that goes along with Jesse Trees.
I think Jesse Trees are a great idea for schools or the home since each ornament can be given its individual due.