It takes time to build trust, at least several months, maybe even years. If you fire everyone before you even get a chance to build up trust with them, you'll never get a great team.
I think it comes down to supply and demand too. If you have 10 qualified applicants, I'd be more apt to fire quick and reach back out to the pool to find a better fit. If it takes 3 months to find a qualified applicant then I'd be more likely to be patient in building trust and working through challenging times. That said, I've fired people after a day on the job. If the hiring process failed, no sense in wasting my time or theirs on trying to create a fit that doesn't exist. Better to move on and fix the hiring process. But don't fire quick and keep your same hiring process, that's just repeating mistakes, rather than being agile.
This is why signing bonuses are so nice, firing someone on day 1 is just awful. If I was an employee at a company who did this to someone I would start looking for another job.
If it takes you years to build trust, maybe you're just not very good at your job. Why should the business take the risk - for years - that you might be trustworthy?