The physical problem with paper
A contract signed on paper exists in a single physical place (or two, one copy for each party). If it gets lost, damaged, or you can't find it when you need it, recovering it can be impossible.
What changes with a digital signature
A contract signed digitally with PAdES stays securely stored, with backups, searchable by client or date, without depending on a single physical copy sitting somewhere in a drawer.
Legal validity isn't an issue
A well-implemented PAdES digital signature carries the same legal weight as a handwritten one, under the law, it's not a compliance compromise for the sake of better organization.
Bottom line
Switching to digital signatures isn't just about signing speed, it's also about the long-term certainty that the important document will be found when you need it.