If I can, can she use it for things like bills or shared expenses between us?
If so, why aren't more people doing this? It seems like an easy way to shelter some money.
No. You will already have paid taxes on the gift you give to your wife, so there will be no tax savings.
A direct gift to a person is never deductible. The kind relative was confusing this with a charitable gift. Which if to a qualified charity can be deducted as part of your itemized deductions. But there, the $14K doesn't enter the equation.
But, if your wife is a dog lover, you can donate to the ASPCA, and give her a note saying "in your honor I donated $14K to the ASPCA." That's a deduction.
If she is unemployed / stay-at-home caregiver, you can squirrel away up to $5,500 in a spousal IRA.
A gift between spouses has no tax implications.
If one spouse dies the inheritance tax is always zero no matter how much of the estate passes to the surviving spouse. Gift taxes are actually related to estate taxes, so a gift no matter how large never requires filing any tax forms or paying any taxes.