I haven't ever offered a settlement agreement to anyone and I genuinely wouldn't ever put someone on a PIP unfairly - I don't even know what people mean when they talk about someone's face "not fitting" tbh. If they can do the job well and collaborate effectively with others, I really don't care about their personality etc. We aren't at work to make friends.
I would only ever go down the PIP route if there were genuine issues that needed to be improved. It's way too much hassle otherwise. A PIP doesn't necessarily mean I want someone out...if they actually improve, then I'm more than happy for them to stay. I start the process wanting it to succeed and wanting to support. But if the employee gets all arsey about the PIP and goes into battle mode, then my own attitude will change and I'll just want them gone. Life is too short to tolerate that kind of negativity.
I'm confident that the processes that I follow are fair and reasonable, and that, if anything, I give people too many chances to turn things around, so why would I offer a settlement? Yeah, it would probably save me some work/aggro, but I don't actually like the idea of rewarding someone for being bad at their job and refusing to try to improve. And I absolutely wouldn't settle if they started trying to deflect from their own poor performance by turning it around and accusing me of bullying. If they wanted to test out their allegations in a tribunal, I would say "bring it on".
The only time I might pay someone to go away would be if they were generally cooperative, willing to try and improve but unable to for some reason. I would feel sorry for them in that situation, and I would want to try and help.
It is never personal for me until someone decides to make it personal. I am as kind as I possibly can be while still doing my job, and I bend over backwards to support people to get their acts together. But if they decide to make it adversarial, then the gloves are off and I will get rid.