Keyboards do not wire to each single key independently. Membrane keyboards use a sort of a sparse grid, which is just enough to tell which key is being pressed right now. Varying by the model, there's about 20 contacts between the membrane and the controller board, including the ground.
Every key being pressed or not is 104 bits of data per poll interval. If the membrane contained semiconductor components that could encode this data, it could send it to the controller. But the membrane is just a plastic film with a bit of silver tracing - a parallel analog interface that has no more capacity than its number of contact pins. The traces are placed such as to identify a couple keys being pressed simultaneously, plus the modifiers.
High-end keyboards are almost universally mechanical, built on a PCB, which supports active electronics at any place on the board. Early mechs included some 6KRO models, but the majority of mechanical keyboards today support NKRO, which means any number of keys will be registered simultaneously.
If you aren't prone to spills and look for guaranteed key registration, the way to go today is mechanical. (With spills, most back-lit mechanicals will die from the high current to the backlight hitting the controller.) There's a small segment that still prefers scissor membrane keyboards, and non-scissor membranes remain the second most spill-resistant practical keyboards after Topre's capacitor models, usually lumped in with mechanical ones.