With today's laptops, is it still necessary to use a laptop cooler cooling pad when it sits on your desk or table?

Oh yes. I guess it depends on the kind of work you do. If you are just browsing, watching videos and stuff, you probably won’t need a cooling pad but if you’re on heavy duty things, you can actually hear the laptop struggling to cope with the load. It starts making weird sounds. It also gets heated up, which you can feel by the touch. I use a laptop to run multiple concurrent apps, that run for hours together, in my line of work. During those times, I sit in a temperature controlled room and run two mini fans, just to cool the lappie off. It is probably overkill….but I don’t want to lose a costly lappie, just because I was careless and ran it ragged. I have no clue about the product you’ve listed though…i just use an AC and two mini fans.

Some laptops run hot – so much depends on the mother board and where they placed the components,

Not every laptop needs extra cooling pads, but many definitely do.

No.
Modern hardware is designed to run hot.
70, 80, even 90°c, all within spec. Fans getting loud? Working as intended. (also unavoidable, because they have to use smaller fans, that have to spin faster to achieve the same cooling performance as a larger fan, and thus are louder).
Manufacturers know that this will happen, because the small formfactor limits the available cooling solutions. That is also the reason why they use special, low-power versions of CPUs and GPUs in laptops.

If your machine runs hot, and you will know when it does, because it will shut itself off to protect itself, you would be better served by opening the machine, cleaning the dust off the fans and cooling fins, and replacing the thermal paste on the CPU.
https://www.ifixit.com/ should have detailed instructions on how to do that. (I would also recommend their toolkit, that is specialised for small electronics devices).

I make sure my laptop is on a flat, hard surface so the vents are unobstructed. On a table, I keep clutter away from it. In my lap, I use a clean cookie sheet I bought for the purpose.

Well, no, my new laptop doesn’t seem to run hot, and it hardly makes any noise at all. I still have the cooling pad with a fan in it that I used to use with my old laptop, but since it’s dusty, I’m thinking (hoping) I won’t have to use it. I sure don’t want to buy a new one if I don’t have to.

Yes.