Another approach to ST_Buffer would be to subdivide the geometries before buffering, and put them all together at the end. ST_SubDivide can do this for us. We can tell it how may vertices we want in each geometry (minimum of 8). Since _ST_BestSRID will try UTM first, we’ll add enough nodes to ensure we always have 8 nodes within the 1,000,000 meter width of a UTM zone by segmentizing at 62,500 meters.

CREATE OR REPLACE FUNCTION ST_Buffer(g1 geography, radius_of_buffer float,
num_seg_quarter_circle integer)
RETURNS geography AS
$BODY$

WITH subdivided AS (
 SELECT
 CASE WHEN ST_GeometryType(g1::geometry) = 'ST_Point' THEN g1
 ELSE (SELECT ST_SubDivide(ST_Segmentize(g1::geometry, 62500), 8) AS geom)
 END
),
transformed_local AS (
 SELECT ST_Transform(g1::geometry, _ST_BestSRID(geom)) AS geom FROM subdivided
),
buffered AS (
 SELECT ST_Buffer(geom, radius_of_buffer, num_seg_quarter_circle) AS geom
 FROM transformed_local
),
transformed_4326 AS (
 SELECT (ST_Dump(ST_Transform(geom, 4326))).geom AS geom FROM buffered
),
checksrid AS (
 SELECT geom FROM transformed_4326
)

SELECT ST_Union(geom)::geography FROM checksrid;
 
$BODY$
LANGUAGE sql VOLATILE;

Aaand, a somewhat unrelated image (just the buffered subdivision of a buffered point, not really an output from our function above. More on all this later.