Is it essential to buy a good CPU cooler?

No, it's not essential to replace your stock CPU cooler. Yes, you can wait and buy a new one later.

I agree with most of the previous answers. Unless you are going to overclock, the stock cooler will probably work for normal use. 

But, if you are going to overclock the stock cooler will most likely be inadequate. Even if you don't overclock, you might want a better cooler if you are going to run number crunching applications for significant periods of time. 

Another factor is the airflow of the case. If you case has poor airflow, and you do a lot of number crunching, your CPU might run hot, whether you use the stock cooler or an improved one.

Here is my experience:

I built the computer I have now 9 years ago. I chose a high performance CPU because I wanted to donate computer time to research. Each research job I was given would run for 2 hours or more of number crunching. But, the bay in my computer desk had a space limitation. I bought a tower case that would fit in the bay. It came with extra fans. But, the airflow was less than I was lead to believe. To keep my CPU cool, I had to limit the research to use 1/4 of CPU power. 

I replaced the case with a large high-airflow case. Because it won't fit in the bay, it is on the floor next to the desk. But, even with the larger case, I couldn't let the research number crunching make full use of my CPU.  I replaced the stock cooler with an all-in-one liquid CPU cooler. I now let the research jobs use 100% of my CPU capacity, with CPU temperature close to 60° C. 

Comment: I donate CPU time through BOINC. https://boinc.berkeley.edu/  Click the "Science Projects" link to get a list of currently available projects. 

You don't need one, but as some other people have said you can get a cheap one for like, $30 that will keep temps lower. Particularly if you have other hot components, or don't have amazing case ventilation. You're still better off getting a good aftermarket cooler. It will drop temps by a lot.

thrift shops have cheap small fans for a couple bucks,be careful to get one that does not short,I used one I thought was OK, it smoked an 1100 watt surround unit ( yamaha). which I need to have serviced

it depends,  my CPU war running 80-90C hot with the stock cooler on my AMD 2700x i upgraded to water cooling aorus 240 water cooler and im running 40C degrees cooler! the cooler you CPU is the better for the processor!!!!

The stock cooler will be fine for now!

If you have a CPU like the Core i7-10700 or Ryzen 5 5800x then the stock cooler will hinder the clock speeds in situations of high CPU usage. Modern CPU's use more power than their TDP rating, but only when thermal limits allow for the CPU to do so. Because of this, a modern CPU might clock higher with a better cooler. With Intel CPU's for instance, The CPU will throttle back on clock speeds and fall back to PL1 when the thermal limits have been reached. PL1 is when the CPU's power consumption will be around it's rated TDP. 

There are plenty of Reviews for Ryzen processors and these newer Core i5 and Core i7 processors that have more than 6-cores that illustrate this point. I would suggest reading up on how AMD's Precision Boost Override and Intel's Turbo Boost 1.0, 20. and 3.0 work before buying a CPU cooler. 

The days of a $330 Core i7-3770k that consumes 60-70w at the most are long, long gone. 

Mostly depends on whether you intend to overclock the CPU.  Stock coolers are fine for most people.  The main benefits of a higher cooler are if you are overclocking or want something quieter than stock. Personally I would pay the extra.

the "stock" cooler is fine for regular use, which is why it ships with it.

but you should NOT mod or overclock your system without proper cooling in place. and be sure there is plenty of space between parts inside your case. tighter cases need more airflow!

Yes, very much yes!

the stock cooler is good enough unless you plan to overclock.  if you do overclock, READ the reviews of your cooler and see what they say about the stock cooler ...

It's fine, just don't overclock it or anything stupid like that.