Where do distributors add value? Not sure.
Do distributors save money for manufacturers? Yes. Here's how it works:
Even though you can buy things online, the different distributors have territory agreements with the manufacturers. Now, cross-territory sales certainly occur, but implied with territory is that they also support customers within the territory. If a distributor sells outside of territory, they might have some travel liability to deal with.
Anyway, let's say a manufacturer sells enough to support an inside sales staff of 10 people for North America. That might cover 10 regions: two in California, one in New York, one for Canada, one for Mexico, and 6 more for everywhere else. The inside sales regions might be roughly equal in yearly sales volume.
Now we have to business options: Sell direct, or sell through distribution.
Selling through Distribution
Each of the 10 inside sales managers works with maybe 3 distributors. Each has a franchised territory. Each has maybe 5 sales and support people. They take care of direct customer issues, whether it's drawing up a quotation, providing training, or making a warranty claim. In effect 3 * 5 * 10 = 150 people are working part-time to support the manufacturer.
Now, while this manufacturer has these regional deals, those distributors have deals with other manufacturers. So they might also sell Keysight, Extech, and some automation equipment. They have diversification by carrying multiple manufacturers across different target price points, industries, etc. This allows their staff to be generally busy to ride out business sales cycles.
Selling Direct
For same same coverage compared to the distributor model, in addition to the 10 inside sales people the manufacturer has their own group of outside sales and technical support. Instead of the equivalent of 150 part-time people, to balance coverage and cost they might need 50 regional sales and support people. Their sales come and go with business cycles, and they don't have diversification across other manufacturers and industries. Now add to this the macroeconomic problem of duplicating this across all the manufacturers that were represented by the distributors. The overall expense is higher, and they will likely face higher overhead and turnover.
They takeaway is that a manufacturer pays the distributor on commission only when a sale is made. If a manufacturer has their own staff, they have to pay all the time, not to mention paying for all the buildings.