People used to take pride in their work, and there was a time when consumers valued quality over price point.

You're never going to walk into a charity shop and find a 100 year old chipboard IKEA wardrobe. Shit is literally made to fall apart and have to be re-bought.

Okay so there are layers to this question:

Why does antique furniture usually have carved feet?

First, antique furniture tends to be the fancy stuff for rich people. Modest furniture made out of a few boards for the unwashed masses usually isn't considered for preservation, but the fancy shit rich people bought got kept.

Rich people tend to like to show off how rich they are. And one way to do that up until fairly recently was through furniture. Maybe you use exotic wood, but even if you don't do that you pay a woodworker to waste his life carving useless intricate details like pineapple newel posts or ornate table legs.

The claw-clutching-a-ball design apparently comes from China, it's supposed to be a dragon's foot clutching a jewel. The British adopted it in the Queen Anne period because it's ornate, fancy and ~~foreign~~ exotic. Rich people get to brag that they got their table, or a taste for the style, "during their travels." Ball-and-claw feet specificall would fall out of fashion with the Chippendale era though fancy schmancyness would hit an all time maximum, and then the industrial revolution happened.

It used to take a skilled artisan to make carvings like that with a chisel. Now, we have duplicating machines that can batch them out dozens at a time. This episode of the New Yankee Workshop shows this off. When building his Lowboy, Norm doesn't even try to carve cabriole legs, he buys them from a company that makes them, and we get a little footage of the factory. This is why you don't see the Zuckerbergs of the world showing off ostentatious carved furniture: ornate carvings are commodity items now. You can buy furniture with cabriole legs and arch cornices at any of those big warehouses out by the highway with a "Going out of business forever" sign out front.

Is it only ornamental?

95% yes. Speaking as a woodworker I can tell you, people overwhelmingly like looking at tapered legs. Our own legs taper, so we tend to copy that. From fancy cabriole legs to simple shaker furniture. A flared foot of any kind is mostly ornamental because again our own feet flare out, but there is a bit of a practical purpose: A larger surface area with a rounded edge is easier to slide across the floor than a small, sharply edged end of a board. It doesn't tend to dig in as much, particularly on carpet. Also, the rounded features are more difficult to chip and splinter.

Why are they usually webbed feet?

It's meant to be a dragon's foot, so somewhere between reptilian and birdlike. It is also furniture, not a statue, so it's rather stylized and not very anatomical. Edit to add, sharp, deep crevices like you get between, say, the fingers of a balled fist, are difficult to carve; The deeper and thinner the crevice, the longer, thinner and more delicate a tool is required to carve it. A craftsman may design around the limitation of the tools he has by, say, making webbed feet rather than trying and failing to do distinct toes.

It's known that the more wealth you acquire, the stronger your foot fetish becomes.

It's known.

Because it’s cool.

Because look at those cute little footsies

Decorative flourish for the most part. A lot of that old stuff was crafted by hand rather than a machine so it tends not to be designed for mass production.

Cause it's freakin cool

That design is known as “Ball and Claw”. It likely originated in the east with some symbolism, but when it went west, craftsman thought it looked cool and started copying it with minor changes.

More info: https://www.furniturelibrary.com/use-of-the-ball-claw-design-motif/

Because they have legs.

Also because SURVIVING antique stuff is still here because it is fancy and well made.

Plenty of cheap shit was made at the same time and long ago burned in the trash pile.

They are the children of Baba Yaga's house.

Cuz looks cool

As for why webbed, because it was easier than carving the toes out completely, and probably more stable.

Webbed toes help them swim more efficiently. As more and more furniture moved indoors, the shape of the legs and feet evolved to the drier climate. You can still find modern pieces where the look has been replicated, but the webbing tends to be decorative in nature, not functional.

What else would they do, hands? That would be silly.

Because it hurts less when you hit your foot against it when going to the toilet during the night

That's just the ones that survived, the others weren't able to run away.