Sounds like this specific e2e suite was poorly optimized and was killed instead of rewritten/optimized due to a perceived notion that inefficiences are inherent in all e2e suites. If you maintain speed and strict curation of such a suite, most of the bullet points against are not an issue.
Also it sounds like the solution is just a bit higher than limited integration testing which does have value of course. Sounds trite, but if you don't test end-to-end you aren't going to catch bugs that only appear end-to-end (which also happen to be the ones customers see making the e2e suite a decent place for high level regressions assuming you maintain test performance of course). This is especially true in environment-specific scenarios.
Also it sounds like the solution is just a bit higher than limited integration testing which does have value of course. Sounds trite, but if you don't test end-to-end you aren't going to catch bugs that only appear end-to-end (which also happen to be the ones customers see making the e2e suite a decent place for high level regressions assuming you maintain test performance of course). This is especially true in environment-specific scenarios.