I'm downvoting you because you stated this as if it is a fact for everyone. We're in a small group plan and paying about the same for Kaiser as we are for Blue Shield, not "much higher". So, I think here's it's more "your mileage may vary."
The whole thing is broken. A friend of mine is switching jobs and is going to forking over a third of her paycheck for COBRA until the new job enrolls her in their plan. Almost certainly, nothing will happen in that short time period, and she'll have wasted thousands of dollars. But if something did happen, and she didn't pay the extortion, sorry COBRA, she'd be up shit creek without a paddle and ruined.
https://www.dol.gov/agencies/ebsa/about-ebsa/our-activities/...
You can enroll after an event and it'll be as though you had insurance the whole time. You'll have to pay for the retroactive coverage, but it's a pretty smooth way (assuming nothing happens) to avoid paying for COBRA while still technically "having coverage".
Though I think there's a time-limit on it.