So your solution to solving one tiny flaw with the GP's otherwise-working setup is to... throw away their monitor, keyboard, and mouse, and spend lots of money (many times more money than an RPi-with-a-hat costs) to replace them?
All because you're offended by the complexity of... what?
• The idea of a device that acts as a stable host for Bluetooth devices, while presenting as a wired USB hub to an upstream USB host controller?
• The particular implementation here, which is a hacky proof-of-concept of the idea (and which could, in practice, be reduced to a single chip embedded into any USB-C-dock product if there was demand)?
• The entire concept of Bluetooth?
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Also, I would like to point out that, given that this is HN, it's more than even odds that the GP:
• likely has multiple monitors (so using a monitor with a built-in hub is likely untenable);
• and also, that their laptops are probably Macbooks, and their mouse and keyboard are therefore very likely a Magic Keyboard and Magic Trackpad [for which there is no 1:1 substitute that does non-Bluetooth wireless while still having the same level of macOS support/integration];
• and that, given what they've said, they're likely already using a Thunderbolt hub to talk to those multiple monitors + all their USB devices through "one cable" (and all they really want is to add one more USB connection to this dock to make it act like a "Bluetooth dock" too);
• and that they likely have a big deep sit-stand desk, that they'd be cluttering/making it hard to put things on the 90% of the free "middle space" on, if they had to run actual wires from the keyboard and mouse over to the dock.