You don't need to put components in your item set lmao
I think we're both understating the number of clicks required to do these things.
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1- click the recommended items page on the left
2- click whatever item has the component you want on the left (ex: you want boots, you click the ionian boots)
3- now look at the right page of the shop, the selected item shows all the components and upgrades related to said item
4- buy boots of choices
Using this way, you must CLICK (1) on a final item that has your desired component, CLICK (2) on the desired component, CLICK (3) on the item that the component builds into (since you're not going to leave an incomplete item in your build, which means you're going to have to do this eventually), and then sometimes CLICK (4) on a different component for that item (if I click on Black Cleaver to click on Kindlegem to get to Spirit Visage to buy a Spectre's Cowl, for example, because I'm building Spirit Visage and I need the Magic Resist Component).
That's 3-4 clicks to buy your first component, one click to buy further components for the same item or complete the item, and 3-4 additional clicks every time you switch which item you're building. If you buy a component for an item (3 clicks), buy Boots of Speed (2 clicks), buy another component to your item (3 clicks), complete your item (1 click), then buy tier 2 Boots of your choice (3 clicks) that's 12 clicks.
Using an item set where you have all your final items, you CLICK (1) on the final item you are building and then CLICK (2) on the component you want to buy.
That's 2 clicks to buy your first component, one click to buy further components for the same item or complete the item, and 2 additional clicks every time you switch which item you're building. If you buy a component for an item (2 clicks), buy Boots of Speed (2 clicks), buy another component for your item (2 clicks), then complete the item (1 click), then buy tier 2 Boots of your choice (1 click because it's a final item in your item set), that's 8 clicks.
You shave off 33% of the time it takes to buy your first item and tier 2 Boots by having an item set prepared.