If we had staff applications, it would increase the workload of the staff, because they would have to take the time to read them all. And while there would probably only be a few applications right now, what about in the future? As the game grows, so would the number of staff applications. It could very well grow to hundreds or even thousands of applications to review. Which will in turn take up more of the staff's time. Thereby hindering productivity and ultimately slowing down future updates and making it harder to moderate the game due to lack of time.
Furthermore, we already have a staff selection system that works. Most of the time new staff are former MOTS and the MOTS themselves are selected by the community. So technically the community already has influence on who gets considered for staff positions.
The current system works and if something is not broken, then there is no reason to fix it. Things that work for other games are not necessarily suitable for this game.
And I also think that staff applications could get spammed by trolls.