In Maxam-Gilbert sequencing, there's no real concern about faithful replication. If the DNA is G-C rich or has a secondary structure, you'll find that the Sanger method cannot replicate the original DNA template. The Maxam-Gilbert method slices the DNA into different sizes and replication is not an issue.
Furthermore, DNA modifications are also a problem with the Sanger method. As an example, a base may have a methyl group attached to it but because you replicate the DNA using extender bases, you would never be aware of the methyl group. The Maxam-Gilbert method allows the identification of these artifacts.
This is achieved using a combination of the Maxam-Gilbert method and mass spectrometry, where the molecular weight of the fragments of the original template are measured. In this way, modifications of the DNA base are easily detected.
The prevalence of kits for Sanger sequencing has undoubtedly made this the method of choice. This is the principal reason why the method is faster and simpler than the Maxam-Gilbert method. Furthermore, mass spectrometry is not required. The fact that the method yields cleaner samples for MS sequencing enabling longer sequences of DNA to be determined, is also a factor in its favour.
The fact that Maxem-Gilbert sequencing data is usually more ambiguous than that produced by the Sanger method is another factor that limits its use. The Maxam-Gilbert method is indeed influenced by reaction impurities and interpretation of the resulting data is more problematical as it requires mass spectometry.
It is also very difficult to find cleavage conditions that consistently give unambiguous and clean cleavage products which is another problem as far as the Maxam-Gilbert method is concerned.
In essence, Chain-Cleavage methods seem to have no place in the future of DNA sequencing.