"Why would either of these solutions be necessary in the first place?"

Mostly because they are quieter. An inline or external blower can also move the air more efficiently by pulling it out of the house instead of pushing it if the exhaust duct is long, or has a few bends in it that cause turbulence to slow down the air flow. Consider stretching out a string, and then trying to move it in a straight direction parallel to its axis by pushing it vs pulling it.

"Shouldn't the blower embedded in the range [hood] be sufficient?"

It is not common to have both an internal hood blower and an external blower working in tandem on the exhaust vent. If the lenght of the vent is long, you would normally switch to an external blower with higher CFM, and a duct with a larger cross sectional area, for example. If the ductwork is too long, with too many twists and turns, warranting the use of two fans, it becomes a fire hazard from all the grease that gets built up in the duct. Many places such as Canada require that the entire duct length be cleanable after installation without removing any drywall etc. If bad duct design and routing is your problem that promoted these questions, I suggest that you find a different solution, or new kitchen design.

The only other reason to have two fans is that the other one is actually for makeup air that blows fresh air into the building when the hood fan is sucking it out. This is now required for any range hood over 400 CFM in most of the US. The new energy codes are even more demanding. In Canada, you need makeup air for any fan(s) including bathroom exhaust that add up to as little as 150 CFM, depending on various conditions.

I don't know why this would be necessary unless you have purchased a massive range that will be in use most of the day (aka the local diner)? And you got the massive range hood to go with it. I have a range hood along with 6" duct work (regular stuff is 4") and about 8-9' from the outside wall, so just a regular old setup. Perhaps you are located deep inside a building somewhere & farther from an outside wall? That could be one reason why they're suggesting this. But yes it would be quieter. Perhaps call in a commercial HVAC person to get another opinion here. And this is an existing building not a new build correct? So requirements may not be as stringent. Inquire with your local building inspector also to play it safe.