Most sequencing methods do use DNA polymerase to effectively copy the DNA while reading out the bases that are being incorporated. However, even when the genome is being replicated in vivo, the polymerase doesn't just copy the entire chromosome in one go from end to end, for various reasons. For example, for larger genomes such as those of animals, it would just take too long to copy it that way. But even for small genomes such as bacteria, DNA replication is still naturally done in fragments. One simple reason is that at any given time the polymerase can dissociate from the template and have to reattach. Even if you could engineer the polymerase to bind more tightly, you'd have to deal with the tradeoff between binding strength, replication rate, and error rate (i.e., a more tightly binding polymerase would likely copy more slowly).