NotUrsula has summed this up well, including the bit about the elderly or infirm being exempt from the rule about not giving cash. Her second point is just as important. It is considered very poor taste to comment (or even to imply, as she said) on someone's financial position. We don't talk money. We can do it on this board anonymously, but that's a whole different matter. Giving money implies you think someone NEEDS money. You may not actually think that, but the implication is there in the South. Also, if someone were to say, "How much do you think this reception cost?," jaws would crash to the ground.
I cannot tell you how many times I have heard the phrase, "It simply is not done," in my lifetime. There are all sorts of things that we are taught from a young age, be we rich or poor, that simply are not done. Our great-grandmothers probably had it stitched on pillows.

Our mothers probably chanted to us while we were in the womb.

It is THAT deeply ingrained, especially in those of us whose families have lived here for a few hundred years.
IT JUST ISN'T DONE!
Break one of those taboos and you hear a collective sharp intake of breath and this is what you see:

Then someone mutters, "Didn't her Mama teach her any better?" and God knows you don't want to shame your mother!

Worse yet, they shake their head and say, "Oh, God bless her poor Mama...." You get the picture.
That's the humorous side of being shamed into compliance, but as NotUrsula pointed out, there are reasons for the behavior. We really do have that explained to us as well.
She is also correct about our receptions just being different in general. I have never once had to check an RSVP letting anyone know which meal I would prefer. Sit down dinners are obviously not as common here. Buffets are more so, and I think with the heat, that may work best. We mingle a lot. Even with a sit down dinner, they may give you a choice when you arrive and they just make sure they have plenty of all choices. A big catering hall isn't that common here.
I did have to laugh about a few of the cake and punch reception comments. Boy, have I been to my share of those! Let me explain. If you have your reception at the church reception hall, and if the church is of certain Protestant denominations, absolutely no alcohol will be allowed. Not even champagne for a toast. Which makes sense....If the religion frowns on drinking, why would they allow alcohol at their church? Such receptions used to be the norm and are still quite common. Get married in the church, go next door for the reception.
I was a rebel and had my reception elsewhere so we actually had champange. Woo-hoo! Wild girl!

I think it was a first for my family, but they all partook. Backsliders!!!!

Not the minister, though. He even politely declined wine at the rehearsal dinner, but that was fine with me. So long as he didn't evil eye the rest of us.
I'm not going to comment on which custom is in better taste, but I can give you an explanation for the reasons why cash gifting is often considered to be tacky in the South.
There are a couple of them actually:
1) A gift of money requires no thought and very little effort beyond earning it. The reasoning is that you couldn't be bothered to make any effort to discover the couple's tastes or preferences, so you just took the easy route and acted as if you were tipping a waiter. (Note that gifts of cash from the elderly are not considered tacky, as forcing them to go out and shop is considered to be burdensome. Of course, if they still maintain homes they often give heirlooms, which are nicest of all.)
2) It implies that you believe yourself to be in better financial standing than the couple, by implying that they actually need money. Any comment on someone else's financial status (even implied) is considered to be in poor taste in that part of the country. This one tends to be the one that makes the average Southerner rear back in horror at the "cover-your-plate" axiom -- the hosts would be appalled at the idea that the guests were speculating on whether or not they (the hosts) could really afford the cost of the wedding; actually, they would be reeling at the idea that the guests were speculating on the costs of the wedding; that isn't done, either, or at least you don't want to get caught doing it.
You should understand that the typical NYC metro area "catering hall" system does not exist in most parts of the South. Many venues are historical buildings that are rented for the occasion and catered by a third party, which may or may not be under contract with the venue. It is next to impossible to accurately guess the menu cost for a wedding in a venue like this, assuming that you even knew what was being served before you arrived, which you normally would not. (RSVP cards that request that guests indicate a menu choice are also very uncommon for Southern weddings -- business dinners perhaps, but not weddings. The norm is that you eat what you are served or you politely pick at it. If you have serious food allergies or are a very strict vegetarian you alert the MOB well ahead of time, and they put you on the "emergency plate" count, and if you're not close enough to the family for that, you just eat before you arrive.)
Oh, also; bridal showers in the South tend to be more about the party than the gifts. Most of them are themed, and the expectation is that the gift will be thoughtful or amusing, but pretty cheap. A chef's apron, a pr. of grill tongs, a piece of lingerie, or a photo frame would be typical. Wedding gifts are presumed to be something that will be used long-term. Things like toaster-ovens are more likely at a working-class wedding; at a middle-class wedding you would see more fine china, crystal and silver.