Looking that old 6.5 CT cutaway, I had a simple and possibly stupid idea: since bullet tip is totally surrounded by plastic case... why don't make it as pointy as possible, in order to improve slightly aerodinamics and armor penetration?

It's not a stupid idea.  The 6.8mm projectile developed for NGSW is about as pointy as possible.

I meant pointy as a needle, not only a nice BC. Like, reducing impact surface as much as possible, less than 1 mm^2

You mean like an APFSDS? I guess that it has been debated here that such formats aren't really useful below some 25 mm, and APDS not good below 12.7.

For rifles and LMG, the 6.5 pictured above is basically as good as it gets.

No, I mean the same specifications as XM1186 but with a pointier point, so to speak. With the least possible point surface

You quickly run into issues with both length to diameter ratio and aerodynamic issues.

Bullets are like aircraft In that their exact shaping determines how much drag they will experience across the various velocity regimes.

What's ideal at 3300 feet per second isn't the same as what's ideal at 1500 feet per second, so you wind up making compromises to get acceptable and stable flight characteristics across the entire range of velocities your projectile could be traveling at when it impacts the target.

As you've pointed out though, you also have to consider it's impact characteristics too.

This puts you in a position where you need to have acceptable terminal performance and flight characteristics throughout a pretty large velocity window.

Because of this, no matter what you're doing it will be a compromise.

In the case of making the bullet tip needle fine, this can create drag and or stability issues that you don't want.

This is why bullet tips are shapes as they are. Unfortunately I can't remember the name of the term specifically for the bullet tip shape and fineness ratio at this time though.

I'm sure someone else will come in and expand on what I've said though.

This is my current bullet shape. full spitzer, no meplat. 

geoffrey-kolbe.com/cgi-bin/drag_working.cgi?unit_length=mm.&weight_unit=grains&bullet_name=GLS+PDW+III&re_calculate=yes&boundary_layer=L%2FT&diameter=6.5&length=20&nose=14&meplat=0&drive_band=6.72&base_diameter=5.5&angle=8.9&boat_tail=3&secant_radius=5.12&weight=34.5&density=5.25

And yes, I agree that CTA would make it possible to have the spitzer actually be 'spitz' (pointy in German).

Hardened Steel penetrator with polymer rest of bullet. My current v0 is 4100 fps, Which I am sure could even be improved upon with CTA and higher pressures. Mind you, I am at ca 560 MPa.

I would like to understand that aerodinamic issues: a really pointy bullet would not be so much different compared with a pitot tube on a mach 2 fighter...

The Pitot tube isn't expected to keep its shape upon impact...

I seem to recall that pointy projectiles tend to break apart even at very shallow impact angles, which means that their usefulness may actually backfire if the impact angle isn't perfectly aligned.