Those aren't curved maps.
See: https://wiki.tfes.org/World_Geodetic_System_1984
Yes they are
There are a number of errors in the wiki and a number of assumptions such as:
WGS84 is a standard coord system its not the best fit, ie one size fits all thats GRS80.
WGS84 is used in simple GPS systems like your phone, its not accurate enough for surveying.
Despite the assertions in the wiki, there is a series of linked local elipsoids. For example the UK uses ETRS89 as the UK is drifting away from WGS84 at a rate of 2.5cm a year, the current total drift is approximately 75cm.
ETRS89 is based on ITRF which itself translates to ITRS the common coord referencing system rather than WGS84. Its independent of any individual government, all of the standard transformational equations are maintained and supplied by the International Earth Rotation and Reference System Service.
Current ITRF is ITRF2019, its updated every year using 4 independent geodetic sources.
The WGS84 and the ITRS do give coords in XYZ not XY as the wiki states.
Moving on to more accurate RE cartesian coordinates you use the geoid, which is the world wide standard base or 0 datum and is within +/- 2m of mean sea level at any location in the world. So for example on the east coast of the UK my zero from the geoid is about -80cm. Datum is set up on local observations, the stations set up triangulate to the geoid which allows accurate transformations made in a standard referencing system.
I do not pretend to be an expert in this field, it is horrifically complicated and full of acronyms, and its been almost 2 decades since I carried out a geodetic survey myself.