I'll give one simple example of a use for whole life:
"Pension Maximization"
You're about to retire, so your company gives you two options for your pension...Option A, and Option B.
Option A says you get $1000/mo, and even if you pass away your spouse will continue to receive it. Option B says we'll give you $2000/mo, but it ends upon your death.
So you buy a whole life policy for a certain amount of coverage (just say $500,000 for example) and it costs you $500/mo to pay for it. Take Option B on your pension, and even if you live many more years, you're still making $500/mo more than Option A, plus your spouse gets $500,000 if you die. Pension maximized, problem solved.
Term insurance is NOT viable for that, you may outlive it and then the ship is sunk.
One last thing, there is NO such thing as an unbiased opinion (ie: Dave Ramsey). Again, his ideals work in an ideal world. I wholeheartedly agree with his logic, it's just that 95% of us won't live his way. His advice only works if you are independently wealthy at retirement.
Actually, it works if you are financially independent at retirement. If you're not financially independent, you can't retire--you have to continue working.