Should infants be allowed in first class?

I am trying to plan a trip to see my parents. Spencer is exhausted, so it would be just me and Olivia on the plane.

Traveling alone with an infant is exhausting. Juggling bags, infant, stroller, and carseat through the X-rays. The physical exertion from carrying the infant. Squeezing into a seat barely big enough for your post-pregnancy arse. Avoiding the beverage cart every time the flight attendants make a pass. Changing diapers on top of a toilet seat. Testing the limits of your bladder to avoid having to use the bathroom while holding an infant. It's hard to get excited by the prospect of flying.

I thought about numerous strategies to make the flight easier. Booking a red-eye in hopes that Olivia would sleep for more of the flight. Booking a flight with a connection in the midwest to shorten the amount of time that I was annoying any one passenger. Booking an extra seat with frequent flyer miles. But, Olivia does not like being put in her car seat, and would probably scream when we try to put her in it on a plane. So, it would probably be a waste of money/miles to get her an extra seat.

Which made me think -- maybe I should use some of these frequent flyer miles to upgrade to first class? That might take some of the pain out of flying, instead of something I feel exhausted just thinking about.

Four years ago when I was a carefree and self absorbed single person, I would have been apalled at the thought. First class is like expensive restaurants, a bastion of perfect silence and British style civility.

To give myself some guidance on the topic, I Googled 'Should babies be allowed on first class?'

I found this article by a guy who believes that babies should be banned from first class. And I found numerous other articles like this one by people who generally associate air travel with screaming infants.

There are also numerous comments from people who point out that babies do not have a monopoly on airplane annoyances. And comments from people who generally acknowledge that as long as you are working to be courteous (and taking trips to the galley when the baby is not happy,) you should be able to sit wherever you want.

Because I'm insecure enough about getting on the plane with an infant as is, I'll probably pass on first class. Probably. Because it is very tempting.... What do you guys think?