US tax: Form 2555: Foreign Earned Income for my foreign spouse

I'm a dual citizen with US citizenship. My spouse is a foreign citizen, who has no US presence at all. Her single source of income is foreign income, my single source of income is US income.

I'm thinking about reporting our tax as marriage filing jointly, and using form 2555 for her foreign income and using her foreign tax payment as tax credit for our US tax. The idea is that since her foreign tax bracket is higher than her US tax bracket, her tax credit would ultimately lower our total US tax.

My question is that:
1. Is my spouse eligible to do this? When she is not US citizen or resident, and she has no presence in the US. I would need to apply for an ITIN for her as well.
2. Is there any downfall for going this route, comparing to just me file my tax as married filing separate?