May I cut in here?

Soccerdad is onto something, a few things actually.

1. Bf doesn't need an "out" to stop talking to his ex, he has free will. And if he doesn't have much of a backbone, just having a gf is enough of an out if he wanted to use that excuse.

2. Bf WILL inevitably feel forced and maybe even resentful. Why? Because as it stands now, it clearly isn't his choice. If it were he would've made it long ago.
With or without gf's discomfort.

3. I sympathise I do. I know what it feels like to be insecure over an ex, even though their relationship was short lived (2 months) and yes I wanted to demand bf never speak to her again. But!!!

3.1 Bf explained that they broke up because they were mismatched as a couple but made much better friends.

3.2 Who am I to dictate who he can be friends with? I have tons of male friends and insecurity aside, I'm sooo not THE type

3.3 I realised that my insecurity was just that. Mine. Something I needed to deal with and not make him responsible for fixing.

What did I do? I actively decided to stop creating issues where there were none.
To trust what I saw infront of me, instead of question what I thought I might not be seeing.

It all boils down to trust.

OP. If you can't find a way to trust your bf yet choose to stay with him, well then I suggest you go ahead and tell him to cut off contact with his ex.
Who knows maybe it doesn't blow up in your face, maybe your bf likes being told what to do.
Seriously, some people are into that.

If he's lucky, maybe then he will be deemed worthy of your trust.