It’s quite (theoretically) easy to get a saw-wave from additive synthesis actually, you add up each harmonic (whole ratios of the base frequency) with an amplitude of 1/harmonic.
The main problem is however how many partials you need in order to replicate a sharp-sounding saw-wave. Naturally this isn’t a problem when you’re just creating the data for a wavetable, but another thing to consider is that the more harmonics you have the playback will be more prone to aliasing. For example if you have geometric waveforms with sharp transitions (e.g a digital square or saw-wave) you typically need to bandlimit the oscillator itself which is very computationally expensive.
For example the Synthesis Technology Morphing Terrarium etc do some pre-bandlimiting in order to avoid aliasing at higher frequencies. In this case they do this in their Wave Edit software by intentionally reducing the harmonic resolution of the wavetables.