See what happened with the OP. They pushed back one week, and are now close to doing it again. As mentioned above there's scope for this to continue indefinitely until the new employer puts their foot down.
Plus, I'm always concerned when a developer ends their last job on Friday and starts Monday at our company.
First several weeks will be ramp-up anyway.
If I want to avoid coverage loss, I'll go with back-to-back employment rather than risk a few days and having to enroll in COBRA.
I'm more concerned about the scenario where a developer has been working 12+ hour days on a release and then 50 or so hours later is now trying to ramp up on at our company.