Rattlesnakes are dangerous pests. Would it be better if they went extinct?

Humans are dangerous threats to rattlesnakes, therefore: - - - - -

they have there place in nature ...............................

First off, they aren't pests but they do help to keep pests in check.  Second, they aren't particularly dangerous.  If you are really careless and ignore their warnings and actually get bit, it is very unlikely to lead to anything but a very sore spot for a while and is quite treatable.  The rattlesnake just wants to be left alone.  

People take rodents as pests also, ans rattlesnakes prey on them.
Get snake smart, they are fairly easy to live in harmony with.
I had them every year about late August.
They are a part of our natural eco system, why upset that with them extinct.
Rattlesnakes are good eating too, yum.

No rattlesnakes have their place in the food web. Given that they are a secondary consumers of rodents, rabbits and lizards to name a few. They help maintain balance in the ecosystem. With them gone the population of rodents, rabbits, lizards etc would increase. Also hawks and other animals eat rattlesnakes and keep them in check. Rattlesnakes rarely bite and only do so if threatened or provoked. 

Rattlesnakes are not pests, because they eat rodents. They are dangerous indeed, but even though thousands of people are bitten every year, the number of people who die from rattlesnake bites are fewer than people who die from bee stings. The actual number of fatalities is low, often fewer than 10.  Cars are a lot more dangerous. Seeking medical help quickly is the key to survival, although it can be very expensive because hospitals charge a lot of money to treat snake bites but they charge a lot of money for practically anything, thousands for a Covid-19 test for example. It is of course better not to have rattlesnakes than to have them, but snakes are very difficult to find in nature. It would simply not be possible to exterminate them totally. People have been rounding up rattlesnakes in many places in the USA but they have not exterminated the snakes locally. A better idea would be to be careful when a person goes out hiking or doing other things in nature. Most people are bitten because they put their hands or feet in places where they cannot see. So, just be careful about doing those things in nature. 

Sure, and let the vermin overpopulate and live in your home

Rattlesnakes asks the same question about humans.

If you think having more small mammals (rodents mostly) in much higher numbers would be "better", then I suppose yes.  But I am not convinced that is "better".

Snakes prey on vermin like rats I'm sure you would enjoy them better