Please consult literally any intro guide to home brewing. They all call for boiling all of the water. I have brewed dozens of batches of beer at home and always boil all of it. I don't know as much about commercial brewing but I've never heard or read of partial boiling as a common technique in commercial brewing. (There is such a thing as "raw ale", but the fact that it has a special name to indicate the lack of boiling tells you it is the exception to the rule).
Boiling is also not only about sterilization. It is also fundamental to the character of the beer. It causes isomerization of the alpha acids in hops which is responsible for the bitter flavors in beer. It also denatures proteins in the wort resulting in clearer beer. See: https://www.love2brew.com/Articles.asp?ID=573
Is it possible that boiling the water and then adding the yeast is a modern practice? People in older times didn't know about yeasts (they didn't know anything about microorganisms). So they couldn't go and buy brewer's yeast from the shop to make beer, they'd have to culture it by natural fermentation. So they couldn't boil the beer before it fermented. Although they could perhaps keep a culture from an early batch and then boil the water of subsequent batches, until they needed to replenish their culture?
That's how traditional yogurt making works. If you ask most people who know how to make yogurt they'll tell you: 1) you boil the milk, 2) you let it cool, and 3) you add yogurt. The yogurt is the fermentation culture (lactic acid bacteria rather than yeasts) and while making yogurt propagates it, at some point someone needs to make yogurt without already having yogurt. The only way to do that is to start with milk that wasn't boiled because boiling kills the culture (the bacteria in yogurt are thermophiles but they won't survive being boiled!). Perhaps something like that happened with brewing also?
Or maybe it's more like modern cheesemaking? Nowadays most cheese is made with pasteurised milk. To make cheese, the milk has to be cultured with lactic acid bacteria, but pasteurisation kills those off. So modern cheesemakers add lyophilised culture to their milk after they pasteurise it. Traditionally though the only way to obtain culture was to leave the milk alone, use it raw. Back in the day people didn't even know about the existence of bacteria so they had no reason to pasteurise their cheesemaking milk in the first place.
So how old is the practice of boiling the water for beer? Is it possible it's something that's only done today thanks to the knowledge of microorganisms?
Boiling is also not only about sterilization. It is also fundamental to the character of the beer. It causes isomerization of the alpha acids in hops which is responsible for the bitter flavors in beer. It also denatures proteins in the wort resulting in clearer beer. See: https://www.love2brew.com/Articles.asp?ID=573