To answer the OP's original question... no, I would never buy a Patek Philippe watch.
For the OP to answer this question, he should ask, "What is the marginal value of this item (product, experience, gift, service, investment) compared to spending/investing/gifting it elsewhere?
Is the marginal value of owning the watch higher than just letting the money sit in an investment? (He probably already has a hundred times this amount in his investments so $38k would be meaningless.)
Is the marginal value higher than doing the 7 continents in 7 days marathons? (Total useless, but a lifetime of bragging rights.)
Is the marginal value higher than gifting the money to a local animal rescue or other charity? To me, bypassing this choice for a watch would result in a lifetime of guilt... unless I donated a bucket load of money to a real charity... not the bloated national charities, but a real local charity that would use most of the money as intended and not go to salaries and perks for the board.
In short, where can the OP get the most value for his $38,000?