Plainly, a lot of oscillators will be necessary to cover the whole audio bandwidth, and this leads to the requirement for a lot of envelope generators as well. Where a subtractive synthesizer (commonly known as an 'analog synthesizer') can get by quite well with just two envelope generators, an additive synthesizer requires one envelope generator per sine wave oscillator so that the level of each of the harmonics can be controlled independently.
The problem back in the early days was that analog electronics were not up to the job. It was impossible to get sufficient accuracy to make additive synthesis work. However, digital electronics can perform additive synthesis just fine.
One idea was additive synthesis. Additive synthesis exploits the fact that any complex sound can be analyzed into its component sine waves (a sine wave is the simplest sound, consisting of only one frequency). Mathematically the reverse would also be true - any sound can be constructed out of sine waves of the right frequencies, levels and phase relationships (timing).