1bit delta sigma modulator has briefly 5 problems. I'll explain all without math and as simple as possible.
But this will oversimplify the content and there might be some questions and errors. So I'll leave some link that will help.
Detailed Explanation Simplified Explanation Practical Example
1. Since there are only 2 levels of output available, there is trouble with printing out low level signal.
This results in dense high frequency distortion and this is
signal-dependant. This distortion looks and sounds like noise(and is treated like noise) since it is so dense in frequency range, but this 'noise' fluctuates depending on input signal. Engineers call this phenomenon 'Noise floor modulation'. This is not 'high resolution' nor 'analog and natural sound'.
2. This problem also happens in '0' input. Even if you just want a silence, a little bit of DC offset made by deviation of electronic parts makes error.
Delta sigma Modulator is similar to a negative feedback circuit. The difference is that in 1bit delta sigma modulator, the feedback signal can be only 1 or 0. So the DC offset error can't be compensated forever.
The link below is a model of simple 1bit delta sigma modulator and you can check out how this works.
link
This results in the oscillation like below
3. On the other hand. multi-bit delta sigma modulators don't suffer from these problems because dither can be applied to them.
Dither noise is a random noise that eliminates the error and adds noise in cost. But this noise is 'natural' as it is constant. The gaussian dither noise is exactly same as LP noise.
However, dither requires
at least additional 2 levels of output. 1bit modulators(with only 2 output level) will be constantly overloaded if dither noise is added into signal.
4. 1bit modulator has more high frequency noise than multi-bit modulator because it needs to shape more noise than 5-6bit modulator. This makes 1bit modulator more sensitive to jitter. In frequency domain, Jitter folds the high frequency signal to low frequency. So the massive amount of high frequency noise in 1bit modulator reduces dynamic range.
Furthermore, this high frequency noise is hard to filter on analogue stage and we need to pay many things(money, resistor noise, complicated circuit, etc) to get a nice attenuation. This is why DAC manufacturers advertise low out-of-band noise.
5. This is the limit of every delta sigma modulator in that they have stability issue when given certain amount of input level.
Every modulator has its modulation depth. 50% of modulation depth means that it can modulate 50% of original signal.
If I convert a PCM file to DSD with a standard modulator that Sony/Philips developed, the volume will be 6dB less on DSD. That's because the maximum modulation depth of 1bit delta-sigma modulator is set to 50%.
From: 'White Paper on Signal Processing for SACD' by two Philips engineer
On the other hand, DAC manufacturers solved this problem by using many tricks. And using multi-bit modulator is one of their trick. Since its SNR is better than 1bit modulator, engineers don't need to use high order modulator to get enough SNR.