A few advantages,
- Standardization It's standardized by the Open Geospatial Consortium (OGC)
- Typing Functions that use a Point are said to accept a Point. So it's advantageous for typing, and working with other libraries. If for instance you need to find functions that work on a Point, search the index on Spatial Relationships and Measurements for 'point' (you can do it now in the browser).
- Indexing while you could index a composite type:
(SRID,long,lat) you'd have a very complex time defining sensible sorts and a custom r-tree index over the composite type.
- Inclusion of SRID A point includes a Spatial reference system (SRID), without which you can't place the coordinate on Earth because you don't know what model of Earth you used.
- Lack of independent standing Lat and Long mean nothing by themselves: what is a Lat:-5.28593 without a corresponding longitudinal coordinate. And, even together they mean nothing without an SRID.
- N-d A Point can optionally include a third or fourth dimension. So it's always a point even in higher-dimensionality space.
- Height? Not a problem (3dz).
- 2d with time? Not a problem (3dm)
- 3d and time? Not a problem. Welcome to 4d
It also provides standardized coercions to and from text use Well-known Text, and to and from binary using Well-known Binary.
As it applies to your leaflet example,
with numerical columns representing latitude and longitude, I'd just filter for all the rows that have a latitude number between the N/S bounds and a longitude number between the E/W bounds, easy.
First, you can't. One degree of longitude converges to 0 as you move towards the pole. Second, even if you could, it would be convoluted. Instead consider the GIS method,
WHERE ST_DWithin( ST_Point(x,y)::geography, distance_in_meters );
Distance in meters! How nice is that. ;)