Under the assumption of Einstein's locality (the observer -you- must
be located in the "center" of the experiment, i.e., you are at the
center of the Mikowsky cone), and using spherical coordinates, couln't
we get rid of one dimension (the radial component of any vector)?

An example: Imagine you (a point-like particle) are in the middle of
space and begin to feel an acceleration. Couln't you describe the
direction you are being pushed with just two components (the two
angles in spherical coordenates). What do you need the radial
component for?

Wouln't spacetime events be described in 2d+time instead of 3d+time ? 

Isn't any point you "see" a projection all over the radius up to infinity?

Your are correct, the direction could be described with just two
components.  The third component, r, is necessary to descibe how much
accerlation there is (to go along with your example).  This is
necessary when dealing with space-time because you must have an actual
value for distance and time to work with it.

Hope that helps a little

Thanks for your comment, Russwolfe. But I'm still not quite convinced.

The acceleration is well defined by the flux of force carriers, i.e.,
by the flux of photons, gravitons, etc. And the energy/momentum of
these particles is defined according to their redshift in frequency.
Once again we need time but nor the r component.