Tim revolutionised the role of Robin. The way he operated independently and how much he grew in the role. He had a lot of freedom.

Would Tim have ever left the mantle if he wasn't forced out?

He operated almost completely solo as Robin a lot. But the culture around Robin in general will always be at the end of "Batman &". Even to this day where the dynamic duo rarely share a page.

Dick left it to be his own man because Robin limited him. Tim has no limits as Robin

Which is why i also think Red Robin is a perfect mantle for him. He made Robin his own and then quite literally made Robin his own.

He acted basically the same as Red Robin as he did as Robin but now the Robin role was free to be filled by someone who needed it.

They had a crossroads.

Make Robin a forever role for Tim and potential cap his potential because Robin will always be seen as Batman's sidekick.

Or make Tim his own mantle. Cementing Robin as a stepping stone but letting Tim go (or continue going) his own way.