You have three kinds of problems wrappped up
in here and my software-socialist hat tells me it's all the fault of poor management:
1. Good software engineering is about writing tools (scaffolding) around the main project (sistene chapel). If a team is not putting in something like 1/3 to 1/2 its time on tooling it is probably being pushed too hard or seeing too many of the other project warning signs we all
know and love.
2. Social contact and pride.
If devs have plenty of time to write their tools, then they get proud of them, make the more generic and usable and they start to market it (hey I have a script that does this is marketing as much as OSS )
Brown bag lunchtime sessions seem the perfect way to encourage this - At a Big Bank we had a kind of show and tell for internal scripts for a while.
3. This is what senior devs, tech leads, what have you, should be doing - talking amoungst themselves and emerging the critical missing parts in the company (besides recruiting and code reviews). Again if they are not - it's a sign of too much pressure, too much silo'd working.
In the end I have some code I happily tell people about and encourage them to use - because I have invested the time to make it work well, and if I have not, I don't coz its embarrassing.
Fix the management / time / good engineering problem and you will find the scripts being shared in the canteen.
Of course fixing that is not something you have authority or influence to do. This could be a problem.