The best balance I have found is to treat the end-to-end test suite as a shared codebase, but with joint ownership. Teams are free to check in to this suite, but the ownership of the health of the suite has to be shared between the teams developing the services themselves. If you want to make extensive use of end-to-end tests with multiple teams I think this approach is essential, and yet I have seen it done very rarely, and never without issue.
How to deal with end to end test ownership: it's hard but make a first class shared code base among rated services covered by tests.

