Typically a legacy trust protects a family from estate tax and creditors. While an effect may be to keep the team in Utah, I would have to guess it was largely done to protect the family from taxes by allowing it to skip a generation, which would make it easier to keep the team in Utah beyond Greg's generation. I've done this for a few families. There are some amazing benefits. Instead of having a beneficiary buy a house, the trust buys it and the beneficiary lives in it. Creditors can't touch it, and it isn't available in divorce to the non-beneficary spouse as it is a trust asset(generally).
The family will continue to be the beneficiaries of the growing value of the Jazz organization, even though the profits are invested back into the team and/or trust. Without seeing the trust to confirm, I'd imagine this was the intent, similar to every other legacy trust I've worked on.
And a legacy trust does not mean the team cannot be sold or moved. Typically a legacy trust is designed to last for generations, but the corpus could be the team or other assets (such as cash for selling the team, which would be reinvested). Often the trustees have a duty to maximize the trust assets as well as a duty to diversify assets. This duties can be largely waived depending on the language of the trust.
Bottom line, doing this definitely does not increase the odds of the team moving, and likely mean it will be around, but the intent I am sure was not purely philanthropic.