As someone in the industry with a lot of exposure to deals like this, I definitely think your second theory is right - Hyatt acquired it to add a long-term management agreement contingency and then remarket it for sale. Not to sound dismissive, but $150M is a pretty small pittance to a company like Hyatt, and does little to offset the balance sheet impact of a $2.7B acquisition. Hyatt is not in the business of owning real estate, and they know that. But they also are smart enough to understand the importance of this one single asset to the overall value proposition of WOH. Ensuring this remains a Hyatt is a win-win for them and their WOH members, and cost very little to do, as you note.
Now, the more interesting question will be "how much will Host influence/dictate how Hyatt runs this property over time?" REITs in general are not known for improving the guest experience, and have the collective reputation of Scott Kirby in his pre-United days. While perhaps not initially, I think they will try to drive ancillary revenues over time and push Hyatt, as their operator, to think more like an owner in the management of Alila Big Sur.