Who says you need Paxos/Raft/etc? What you describe is essentially a distributed, atomic Compare-And-Swap operation. You could use any number of mechanisms to do so and a SQL database will work just fine. Your idea for adding in an additional timestamp that must be continually refreshed to retain master status is a common pattern in this arena and it's often referred to as "Master Leases".
Depending upon your application and it's intended operating environment, using a designated third party to arbitrate between peers (which is the role the SQL database fills in your example) might be your best option. It introduces a single point of failure but it's super simple and periodic downtime maintenance windows may be tolerable, again depending on the application. The potential advantage of something like Raft or Multi-Paxos is that there is no single point of failure. As long as a quorum of peers are available, the ability to choose and maintain the master peer is available. The up-front implementation is probably an order of magnitude more complex but you remove the single point of failure and gain a measure of overall architectural simplicity by removing the concept of the designated 3rd party.
Ultimately, it depends on what you're trying to do and the level of robustness you need. Is the maintenance burden and potential downtime of a SPOF a deal breaker for your app? If yes, go Raft/Multi-Paxos. If not, honor the KISS principle and go the designated 3rd party route.