[racer_d]

That is a practice called "double de-clutching".

Race cars typically have "straight cut" gears. Passengers have "curved" gears, and synchonizers. The job of the syncrhos is to make double de-clutching obsolete.

Can you do it without harming your car? Yes, absolutely. It is also an integral skill in heal-toe downshifting. But, it is not necessary.

The goal of "blipping the gas" is to ensure that once you downshift into the lower gear, the engine will already be spinning at the correct rate. It makes for smoother downshifts.