The well paying companies have no trouble hiring
someone good, but I wouldn't say they have
"their pick" of employees. There are a lot of people out there who politely decline or ignore every approach from FAANG recruiters, for example, because the mission or company are unattractive and high pay doesn't make up for it.
So from a statistical perspective you can say that paying well means they have a lot of people to choose from. But some types of mission are greatly affected by the few particular people who are really specialised or inspired in some area or another, and those people aren't always willing to give up their personal dreams to work for an unattractive company just for a larger pay packet.