Looks like you've found your answer, by investing in a Roth IRA. But thought I'd answer this anyway:
Here is what I don't get: if I put $5500 into my traditional IRA today using money I have in a savings account, where is the tax advantage?
If you made well over the limit for tax deduction, you still get tax deferral. Consider Vanguard Total Bond which yields about 2%. In your after tax account, you pay 1/4th of the 2% yield in taxes. But if you have a Traditional IRA, you delay paying taxes. Instead of taking 0.5%, the IRS lets you keep that money and compound it.