How to reduce points by proximity

Maybe is not the fastest way but you could achieve this in three steps:

Convert your points to raster: Raster -> Conversion -> Rasterize

Reduce the resolution: Raster -> Conversion -> Translate (Outsize)

Convert your resized raster back to points again using the SAGA pluguin. Algorithm -> Grid values to points.

However, I'm still not sure about what you want to accomplish, as @Simbamangu said usually it is not a good idea just to eliminate data. Maybe you need to average, sum, interpolate...