Back in the 9s and 10s eras, my recollection (which could be mistaken) is that cassettes starting with 12t were common, although gearing was 53/39. Professionals used cassettes starting with 11t. A 53/12 gear was regarded as more than sufficient.
In the mid 2000s, we started to see compact (50/34) cranks. Those were paired with cassettes starting with 11t cogs. As compact and subcompact (52/36) cranks started becoming more common, my recollection is that most cassettes eventually migrated to 11t starting cogs; a 50/11 is the rough equivalent of a 53/12. Why not provide more cassettes with 12t starting cogs? I've wondered this myself, as I'd like to pair a 52/36 subcompact with, say, a 12-28 or -30 (11s) cassette. However, for Shimano, 12/28 cassettes are only available in Dura Ace, and Campagnolo may have one Centaur-level 12-xx cassette. As to the question of why all cassettes seem to start at 11t, I have a feeling that this is because most amateurs have probably shifted to 50/34 chainrings (or the equivalent in SRAM's AXS gearing, which I think is 46/33 with 10t starting cogs).
You are correct that the smaller the sprocket, the more the drivetrain friction. I believe the primary contributor to friction is actually how much the chain is articulated around the cog. The impact of cross-chaining is smaller, if I remember correctly. If you wanted to investigate this, you'd have to dig up reports from Friction Facts (some of which may be available on the CeramicSpeed website; remember that CeramicSpeed bought out Friction Facts and its owner, Jason Smith). However, we only started to pay attention to drivetrain friction recently. I suspect path dependence is part of the reason why they haven't shifted to larger cogs and chainrings. In political science and other social sciences, this is the notion that past decisions constrain future decisions as institutions and technology become adapted to the choice - in this case, a lot of it would be the tooling, and no small part would be consumer expectations.
As to the question being asked: if you're asking if it's technically possible for consumers to build their own drivetrains with 13/14t starting cogs and commensurately larger chainrings, it could be. But you'd be talking about contracting with someone to make the cogs and rings. Given the patents around the shift ramps, you'd probably be talking about unramped cogs and chainrings, which would worsen shifting. Also, consider that while you do pay a friction penalty for being in small cogs, it's most prominent in 11t or smaller cogs. Most amateurs are rarely in these gears. If they are, it's most likely downhill. The wattage penalty to an equivalent 53/12 gear is probably small, and also you are probably at the speed where it may be preferable to just coast (since the power to overcome aerodynamic drag is proportionate to velocity cubed).