It sounds to me like you have used one particular kind of mechanical keyboard. What you describe sounds a lot like either a buckling spring like the Model M or a clicky tactile switch like the Cherry MX Blue.
One of the cool things about mechanical switches is they can be built in such a way to have different characteristics. Much like how a car's suspension can be tuned to be soft or hard and with high ground clearance or low down you can build switches to be loud of quiet, clicky or soft, long or short travel.
As for why they are appealing, many people like tactile interfaces with positive feedback. In a world where everything is a touch sensitive slab of glass its nice to interface with something mechanical and responsive instead of a lifeless slate. Its the dexterous equivalent to ASMR. Its why people like manual transmissions, bolt action rifles, physical switches and knobs.