What is the point of clay or porcelain teapots that you put on the table?

It is more for show these days, than practicality. 

Teapots are usually for a group of people. That's a lot of tea for one person 

We make a pot of mint tea almost every night in the winter. A decent sized pot. The 1st cup is too hot to drink, the 2nd cup is a perfect drinking temperature. The last cup is lukewarm, so sometimes we drink it, sometimes we quickly nuke it. In other words, I don't have the problem you have.

It's not a dumb question it’s just that you don't understand how a tea pot was/is used. 

Tea bags are a relatively recent invention.the idea of a tea pot is that the loose tea is placed in the pot and infused in boiling water for a few minutes and then poured out. You might end up with a few tea leaves in your cup but most stay in the pot.

The tea is “made” in the tea pot and then served. It's like having punch at a party - you'd make it in one container, not in each individual glass. Making a pot of tea for several people is far easier and less wasteful than trying to make several cups separately.

If there is a group of people they can choose their own combination of tea, milk and hot water (often served in a separate pot). Much easier with a pot than trying to do it with separate cups/mugs.

When in a cafe, restaurant or tea room the tea is brought in a pot, with a lid and poured out by the customer at the table. If they want a second cup then it's there for them.

Tea keeps a lot hotter in the tea pot than in a cup. If you ordered, say, a cup of tea and a piece of cake or a scone or something inna restaurant tea in a cup could be cool by the time the order reached you (and it might have been coughed on or sneezed on).

Tea made correctly with boiling water in a warmed tea pot (especially with a tea cosy) stays hot enough.

I'd never bother with a tea pot if making a single cup of tea for myself but if two or three of us are having tea a teapot is useful, even though I use tea bags.

thats actually a good question. i think its just for decoration. usually the glass tea kettles are the best and then people pour into the clay ones for aesthetics. half the time its just as useless as a flower vase. ( not useless like bad way)

i have learned one thing though. the glass kettles get hot . I burned the handle of the tea pot lmao, now i put a wooden spoon to seperate  the handle  from the glass. because it gets hot.

oh and also what appears to be porcelein is actually metal with a fake cover. 

if metal and glass are damaged then i dont think real porecein will survive lol

thats why its just for aesthetics. but good for drinking as soon as it is poured.

Ever hear of a tea cozy? It is like a coat for the teapot.