The absolute best case scenario for using a 1-4 FNA is avoiding spending 18k points, which would cost you $390 to buy during the current poor 20% bonus promotion. Most people don't manage to use their FNAs optimally and/or hit their annual cap for buying points during the best bonuses.

You are going to spend at least half of that on taxis, Ubers, etc. to hotel hop every day. Not to mention the loss of holiday enjoyment.

You wouldn't even be missing out on anything - you have a lifetime to collect brands organically.

There is no "making the math work". There is "I like to do silly things in the miles/points hobby because they make me feel good"

There are some less extreme options, however. I can see staying one-night at the Vivid in Cancun because you're arriving late or departing early and want to be close to the airport - but spending the rest of the trip in your preferred hotel.