I believe there was no long-term thinking behind Ole's permanent appointment. Remember at the time he was caretaker, they said they would be conducting a thorough hiring process for the next manager to be appointed in the summer. Even Ole said at the beginning that he was planning to leave in the summer.
But we never actually saw any signs of this process did we? When he was made permanent manager on 28th March 2019, a few weeks after that PSG win, it was off the back of two consecutive defeats (Arsenal & Wolves in FA Cup). Isn't that very strange? What was the mad rush to appoint him?
If we was supposed to be interviewing other managers in this period, why wouldn't we continue to wait until the end of the season, especially when we're seeing the first signs of the wheels falling off? I don't think people remember just how bad Ole was after he was made permanent. We played 10 matches, winning just 2, drawing 2, and losing 6 with a 2-0 home loss to relegated Cardiff on the last day.
The only answer I can come up with, is that on his initial run, the club saw a chance to take a cheap punt on him, because he came with benefits. As a manager who was indebted to the board for even choosing him to begin with, after Mourinho, they knew he would never ask for much, or make them look bad in public. He would let them renew players like Jones, Young, Smalling (all signing on Ole's watch) to 'preserve their value', instead of demanding reinforcements. And most important, as a former legend, he would serve as a lightning rod for fan's discontent toward the board.