When has this strategy led to long term, sustained success?
A fundamental issue with low admissions pricing is that it invites the wrong kind of customer - frugal or price sensitive families, parents looking for cheap summer day care, etc. - who are unlikely to spend frivolously regardless of how things are priced inside the gate.
Giving away the gate also squanders a unique advantage these regional parks have, which is that they are down market of Disney-level entertainment options, so if/when economic conditions lead to a softening of demand on the higher end, they can absorb that business, giving up the lower end customer to FECs and the like.
Another fundamental problem is that it takes a long time and effort to build gate integrity. Demonstrating to customers that your product is worth the elevated price point you're charging can take years, even generations, and all of that is completely undone in an instant by lowering the gate price. Once the gate integrity is destroyed, declining revenue and per caps, and attendance when the economy softens, make it virtually impossible to correct course before bankruptcy is the only option.