Open sourcing code can require a lot of resources to do it right (manage the community, handle licensing etc). If you don't have customers asking for it and you don't need it for customer acquisition it might not make sense.
Open sourcing does not mean you want or going to accept external contribution, just be explicit that you don't accept external contributions.
There are several open source projects that are developed with no public contribution policy. Nothing new to invent here.
No, this is how you get seriously annoying divergences in products like this. GPL2/3 would be 10/10. It would also protect the company too.