I think it largely depends on how do you fire people.

If you just decide 'fuck it, he's out' than yeah, that's awful. But if you give a chance to correct the issues, and actually give the chance rather than imposing some impossible requirements with your mind already set, that's different. Sometimes you just need a little push.

>>> Firing people frequently is also expensive and it's demoralizing for the team

Not sure about the expensive bit (it's better to fire sooner than later if you're going to fire anyway), but also concerned about the morale. Unless that's a very rare occurrence for quite obvious reasons, it will no doubt demoralize the team.