Aluminum profile and alu plate 1500mm x 600mm x 150mm working area, first cnc.

[JAZZCNC]

I believe ~10m.min is very good for a DIY machine, not servo driven. i would not trust steppers for faster speeds. Also there is that thing that the machine to benefit from the fastest speeds it must be big. See the formula at the bottom of that page

Fact using stepper doesn't mean can't have higher feeds. The feeds depends on pitch. Could have 50,000mtr/min quite easily and still have acceptable acceleration with the right pitch.
What stepper does restrict is having High Feeds and High Resolution. The price you pay to achieve high speed is Low resolution.

Also To answer your question if Stepper can achieve 3000mm/s/s and 15,000mm is yes.!! . . . . . . Could it do this and hold the same resolution at your size/weight of machine then No.!! . . . Hence why you wouldn't fit steppers.

However on smaller machine with lighter gantry then yes it's possible with careful selection of pitch and motors etc.

Good machine will have nice balance of speed and Acceleration. IME for Medium machine size which this is, 10,000mm/min and 1500mm/s/s is all thats required.