Companies rarely have an interest to get in a bidding war because the best outcome is that you pay a lot to hang on to that person for a little while longer. People at that level more often leave because their job was done and they want new, interesting projects, money alone won't cut it. The worst outcome is that it incentivizes more employees to try the same approach. The company either opens the spending floodgates, or rejects a lot of them thus losing people either to the competition or to demotivation.

When it's one person they probably rely on the fact that the team and structure in place can take a loss. When it's a mass departure they will give bonuses as they have done recently with the possible departures to Meta.